{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "00f1c4ba",
   "metadata": {},
   "source": [
    "# Robust Linear Regression\n",
    "\n",
    "This example has been lifted from the [PyMC Docs](https://www.pymc.io/projects/examples/en/latest/generalized_linear_models/GLM-robust.html), and adapted to for Bambi by Tyler James Burch ([\\@tjburch](https://github.com/tjburch) on GitHub).\n",
    "\n",
    "Many toy datasets circumvent problems that practitioners run into with real data. Specifically, the assumption of normality can be easily violated by outliers, which can cause havoc in traditional linear regression. One way to navigate this is through _robust linear regression_, outlined in this example.\n",
    "\n",
    "First load modules and set the RNG for reproducibility."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "6eb36093",
   "metadata": {},
   "outputs": [],
   "source": [
    "import arviz as az\n",
    "import bambi as bmb\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "az.style.use(\"arviz-darkgrid\")\n",
    "\n",
    "rng = np.random.default_rng(1211)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "21b9a74d",
   "metadata": {},
   "source": [
    "Next, generate pseudodata. The bulk of the data will be linear with noise distributed normally, but additionally several outliers will be interjected."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "b3b8fb29",
   "metadata": {},
   "outputs": [],
   "source": [
    "size = 100\n",
    "true_intercept = 1\n",
    "true_slope = 2\n",
    "\n",
    "x = np.linspace(0, 1, size)\n",
    "# y = a + b*x\n",
    "true_regression_line = true_intercept + true_slope * x\n",
    "# add noise\n",
    "y = true_regression_line + rng.normal(scale=0.5, size=size)\n",
    "\n",
    "# Add outliers\n",
    "x_out = np.append(x, [0.1, 0.15, 0.2])\n",
    "y_out = np.append(y, [8, 6, 9])\n",
    "\n",
    "data = pd.DataFrame({\"x\": x_out,  \"y\": y_out})"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9b2c491c",
   "metadata": {},
   "source": [
    "Plot this data. The three data points in the top left are the interjected data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "5251d460",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAscAAALHCAYAAABi9u8uAAAAOnRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjEwLjYsIGh0dHBzOi8vbWF0cGxvdGxpYi5vcmcvq6yFwwAAAAlwSFlzAAAPYQAAD2EBqD+naQAAhtRJREFUeJzt3Xd8U+Xix/FvkhZKKZQyC8hSaGWUrSAgCIgTBw7koiLLvddV73Vc/blRrwLiZAhXEBGc4AAVEZQ9WpYgexUKLS1tGW1yfn/0JDRtOkmz+nm/Xr6kSc45z8mTtN/znGdYDMMwBAAAAEBWfxcAAAAACBSEYwAAAMBEOAYAAABMhGMAAADARDgGAAAATIRjAAAAwEQ4BgAAAEyEYwAAAMBEOAYAAABMhGMAXrV3717Fx8erX79+Xt1vv379FB8fr71793p1v5VZfHy84uPj/V2MM3LrrbcqPj5ey5YtC8pjzpkzR/Hx8XryySe9UDJI0pNPPqn4+HjNmTPHK/vjd0/lE+bvAgAlSUxM1JdffqkVK1bo4MGDys7OVlRUlFq0aKHOnTvriiuuULt27fxdzICzbNkyLV++XOeff766devm7+IElIyMDH3yySeqUaOGhg8f7u/iAAACCC3HCFjHjx/Xo48+qhtvvFHTp0/Xzp07VbduXbVp00bR0dFKTEzUxIkTdf311+v222/3d3EDzvLlyzV+/HgtX77c30UJOBkZGRo/frymTp3q76KgkqtRo4ZatGihevXq+bsoAEy0HCMg5eTkaNSoUVq1apXq1aunhx9+WJdffrkiIyNdr8nIyNDPP/+sjz/+WEuXLvVjaQGgfAYMGKABAwb4uxgA8iEcIyCNHz9eq1atUv369fX555+rYcOGhV5Ts2ZNDRo0SFdddZU++ugjP5QSAACEGsIxAk5GRobrdvfTTz/tMRjnFxYWprvvvrvI53///Xd9+umnSkxMVEZGhmrXrq2ePXvq7rvvVtOmTd1eu3fvXvXv31+NGzfWL7/8oq+//lqffPKJtm3bpqpVq6p79+56/PHH1aRJE4/HOn78uKZNm6YffvhBO3fulN1uV/PmzXXVVVdp2LBhqlKlitvrx40bp/Hjx+u+++7TzTffrPHjx2vhwoU6ePCgrrrqKr366quSpCVLlujnn3/WypUrlZycrOPHj6tBgwbq2bOn7rzzTjVq1Mhtv/kHWY0fP17jx493/Txo0CDXfiXJMAzNmzdPX3zxhTZu3KisrCw1aNBAffv21Z133lnk7d7ly5drwoQJSkxMlMViUZs2bXTXXXepWbNmRdZFSfbt26f//ve/WrJkibKzs9W0aVMNGTJEQ4cOLXKbPXv26Pvvv9fvv/+u3bt368iRI4qKilLbtm1166236qKLLnJ7/ZNPPqkvv/zSdbyCA9L++usvSdKJEye0YMEC/fzzz9q4caMOHTokSWratKkuvfRSDR8+3O1ORmmkpKTohx9+0MKFC7Vjxw6lpKQoIiJC8fHxuuGGG3TttdcW2uZMP5ObN2/WO++8o5UrVyo3N1ctW7bU8OHDdeWVV5ap7E7O98v5PhXUr18/7du3Tz///LPOOussj48fPnxY48eP17p165STk6M2bdro/vvv1wUXXOBxn6mpqRo7dqx+/vlnHT16VI0aNdLVV1+tO+64o8Tynsn3//PPP9fMmTO1fft2ZWdnF3nOkjR48GCtW7dOY8eO1aWXXurxNRMnTtTrr7+uSy+9VGPHjpWUNyDvqaeeKvS9XLZsmYYNG6bzzz9fn3zyiaZNm6ZZs2Zp165dqlGjhi666CI99thjql27tsdj/fnnn3rvvfe0fv16Wa1WtW3bVnfddZeaNGnido6llb/e58+fr4kTJ+qvv/5StWrVdOGFF+qxxx5z/a6YPXu2Pv30U23fvl3VqlXTgAED9Pjjj6tGjRoe97169WpNmjRJq1evdtVR9+7ddeedd+qcc87xuE12drbee+89zZ07VykpKapXr54uueQS3X///SWeS2JioiZPnqyVK1cqLS1NNWvWVNeuXXXXXXepTZs2pX5PELoIxwg4v/32m7Kzs1WvXj1dfPHFZ7Svl156yRW069Spo1atWmn37t2aM2eOfvrpJ3300Ufq3Lmzx23ffPNNffjhh2rcuLGaN2+u7du368cff9Tq1av1zTffFPqjdPDgQY0cOVJ///23wsLC1LhxY4WFhenvv//WmDFj9Msvv2jSpEmKiIgodKzU1FRdf/31OnjwoFq2bKmoqChZraeHBNx+++1yOByqXbu2GjVqJLvdrr179+qzzz7TDz/8oE8//VQtW7Z0vb5z5846cOCADhw4oIYNG7pdYDRv3tz175ycHD322GP64YcfJEn169dXbGysdu3a5Qr506ZNU4sWLdzKO3fuXD322GNyOByqVauWzjrrLG3ZskWjR4/Www8/XMracbdt2zYNHTpUR48eVdWqVdWyZUulpaXphRde0N9//13kdu+//76++OILRUZGqn79+oqPj9fBgwe1ePFiLV68WI8++qhbiGrevLnatWun9evXq0qVKkUO5ly/fr0effRRhYWFqW7dujr77LOVmZmpv//+W5s3b9aCBQs0ffp0j/VZlFmzZumdd95RRESE6tevr7i4OKWmpmrFihVasWKF1qxZo+eff77I7cv6mVyxYoVGjx6tEydOKCoqSmeffbYOHDigRx55RAcOHCh1ub1p4cKFevXVV1W9enU1adJEu3fv1qpVqzR69GhNmjSp0ODRlJQU/eMf/9CePXsUFhamVq1a6fjx4xo7dqySkpJkGEaRxzqT7/9zzz2nzz77TA0bNtTZZ5+t3bt3F3te119/vdatW6cvv/yyyHD81VdfSZKuu+66YvdV0OOPP67vvvtOzZs3V7NmzbRjxw7Nnj1biYmJmjNnTqGL7q+++kpPPvmkDMNQTEyMzjrrLG3evFkjR47UY489VqZjFzRt2jS9+OKLio2NVdOmTbV9+3Z99dVXWr9+vebMmaMxY8Zo2rRpatKkic466yzt2LFDM2fO1I4dOzR16lRZLBa3/U2fPl0vvPCCDMNQnTp1FB8fr927d+vrr7/WDz/8oLFjxxa6wM3OztZtt93mujBv1aqVHA6HpkyZouXLl7v9jitoypQpevXVV2UYhmrVqqVWrVpp//79+vHHH/XLL7/orbfe0iWXXHJG7xFCgAEEmOeff96Ii4sz7r333jPaz4wZM4y4uDijX79+xtKlS12P5+bmGhMmTDDi4uKM3r17GydOnHA9t2fPHiMuLs5o06aN0blzZ2PhwoWu5w4dOmRcddVVRlxcnDFmzBi3Y9ntduOmm24y4uLijIcffthISUlxPXfgwAFj6NChRlxcnPHqq6+6bTd27FgjLi7OaN26tXHTTTcZBw4ccD2Xv1yfffaZkZyc7Lbt8ePHjffee8+Ii4szbrnllkLn79z32LFji3yP3njjDSMuLs649tprjY0bN7rt+z//+Y8RFxdnXHfddW7bJCcnGx07djTi4uKMN954w8jJyTEMwzBOnTplvPzyy0bbtm2NuLg4o2/fvkUetyCHw2EMGjTIiIuLM0aOHGmkpaW5nvvuu++Mtm3bGm3atDHi4uKMPXv2uG27cOFCY+3atYbD4XB7fMWKFUbPnj2N1q1bG7t27XJ7zlnPxZVx7969xrx584zMzEy3xw8dOmTcf//9RlxcnDFu3LhSn6OzTH/++aeRm5vr9vimTZuMyy+/3IiLizOWLVvmsaxl/UxmZWUZvXv3NuLi4ox//vOfRnZ2tmEYeZ/VSZMmueopLi6uTOdQ0jZ9+/b1WE/Ox9u2bWt88MEHrvfg1KlTxqOPPmrExcUZN954Y6H93XvvvUZcXJwxaNAgY//+/a7H//jjD6NTp06u88j/HTeMM/v+t27d2ujYsaOxYMEC13PHjx93/fuWW24pdMxjx44ZHTp0MNq0aWMcPny40HmsX7/eiIuLM3r27OlW/7Nnzzbi4uKMJ554wu31S5cudb1fvXr1MtatW+d6bvv27a66nT59utt2+/btMzp06GDExcUZ//3vf13HysnJMd54441yfT8N43S9d+zY0fj2229djx84cMAYMGCAERcXZ9xzzz1Gly5djD/++MP1/ObNm43zzz/fiIuLc/vsGoZhbNy40fW9/uijjwy73W4YhmGcPHnS9funS5cuxsGDB922e/nll13nsGXLFtfjmzZtMi688ELXOc6ePdttu99++82Ij483unXrZvz4449uz33++edGmzZtjE6dOhU6XlGfaYQuZqtAwDl48KAkqXHjxuXex6lTpzR+/HjZbDaNGzfOrTXKZrPp7rvv1qWXXqrk5GR9//33hbbPzc3Vfffdpz59+rgeq1evnh566CFJ0qJFi9xev3DhQq1Zs0YJCQl6/fXXVbduXddzsbGx+u9//6vIyEh99tlnOnHiRKHj2Ww2vfPOO4qNjXU9VrVqVde/b7rpJjVo0MBtm4iICN11113q0qWLli9f7nrfSis1NVVTpkxRVFSU3nvvPbVu3dpt388884wSEhK0fv16rVy50vXcjBkzlJ2drYSEBFfLqiSFh4frqaee0tlnn12mckjS0qVLtWHDBkVERGjMmDGqVauW67krr7xSQ4YMUW5ursdt+/Tpow4dOhRqkeratasefPBB2e12zZs3r8xlaty4sS6//HJVr17d7fF69erp9ddfV3h4uL799tsy7bNr167q3r27bDab2+PnnnuunnnmGUkqcp9l/UzOnTtXycnJatCggV588UVVq1ZNkmS1WjVixAhdeOGFZSq7t/Tq1Ut33HGH6z0IDw/Xv/71L1WpUkXr1q1Tenq667W7du3SggULJEmvvfaa2x2QCy64QA888IBycnIKHeNMv/92u10PPPCA+vfv73qspDsEUVFRuuSSS5Sbm+uxDp1dea666qpC9V+cnJwcPfPMM2rfvr3rsRYtWmj06NGSCtf7jBkzdPz4cfXo0UMPPfSQ61hhYWF69NFH1alTp1If25MbbrhBAwcOdP0cGxurUaNGSZIWLFig++67z617THx8vAYPHiwpr4tLfhMnTlRubq769++v0aNHu+6WValSRc8++6xatWqlY8eOacaMGa5tMjMzNXPmTEl5rfutWrVyPef8Hnn6TEjS22+/LcMw9NJLLxVqHb7xxhs1bNgwZWVladasWWV+XxBa6FaBgJOVlSVJrj/mBc2dO1ePPPJIocdfeeUV1+3KtWvXKiUlRQkJCUX2IevXr59+/PFHrVixwmNfzxtuuKHQYwkJCZLy+rnmN3/+fEl5/XmdYTG/+vXrKyEhQcuWLdP69evVtWtXt+d79OhRKPwWlJSUpB9//FF///23MjMzZbfbJeUFCCmvb2lJ+8jvt99+06lTp9SvXz+3UO5ktVp10UUXKSkpScuXL3eVefHixZKkf/zjHx73O3ToUD333HOlLod0+o/mZZdd5rEP5dChQzVt2rQit09NTdW3336rxMREHTlyRCdPnpSU94dUyntvysPhcOiXX37RkiVLtGfPHmVnZ7tu41ssFu3cuVPHjx8v8rPqSWZmpubNm6dVq1YpJSVFJ06ckGEYOnXqVIllLctn0llPN9xwg8LDwwttN3To0DL1OfWWG2+8sdBjtWvXVuPGjbVjxw7t2bNH0dHRkvLOwTAMnXfeeW4hyOmGG27QG2+8USgMeeP7f80115T53K6//np9/fXX+uqrr9zmz87JydHcuXMllb1LRXR0tMfb/M56L7gwxZIlS4o9znXXXXdG0zt6+gzmv7Au7vmiynrrrbcW2sZisejWW2/Vs88+qyVLlujBBx+UJK1atUrHjx9X48aN1bt370Lb9e/fXw0aNCjUWLBv3z5t2LBBderUcbvoya9fv36aNGmSVqxY4fF5VB6EYwQcZ0vd8ePHPT5fu3Ztt36CW7du1bFjx9xes2XLFkl5vxCLCnHObTy1uMbExHgcPFKnTh1JeX3e8nMO1Pnss8/03XffeTzezp07Jck1sCu/4lpbDcPQCy+8oOnTpxf5GkluLW6l4XyP1q1bV+R7dOTIEUnu75HzPIoaKFPU48UpaZ/NmzdXWFiYx9bjxYsX66GHHir0GcivrO+NlDcw9I477tCaNWtKfF1pw/HGjRt15513evwMOBVV1rJ+Jiuinryh4CA4pzp16mjHjh1u5+E8h6K+H1FRUWrQoEGh0OWN739RA92Kc/7556tp06batGmTNm/erHPPPVdS3oVoamqq2rVr5zHkF6eogZbOenc2Jjg5L5aLWvnwTFdE9FR/MTExkvJ+N0dFRRV63vle5i9rRkaGUlNTJRX9WXSOo3B+DiRpx44dkvJazwveLZLyLuqbN29eqF6dn4mTJ08W+ZlwXlSX9S4cQg/hGAHH2fq5b98+j89fcMEFbrfthg8frj///NPtNc4/fKmpqa5fwEVx/kLMr6hZCPIPksvP2ULp/AVcHE/dKoqb9eDrr7/W9OnTFRkZqccff1w9e/ZUgwYNXLd5H3vsMX377bdFdjsoivM9cg7cK07+98gZXooKD84/2mXh3Kfzj2xBVqtVMTExSklJcXs8IyNDjzzyiI4dO6Zrr71WQ4cOVYsWLVwDGv/44w+NGDGizO+NlHcnYs2aNWrRooUeeeQRdejQQTExMa7BT71799bBgweLvIVbkN1u10MPPaRDhw6pT58+uv3229WyZUvVrFlTNptNu3btct2W96Ssn8mS6il/1x9fKupCwnkeRr4BdiWdg5R3HgXDcUV9/0tisVg0aNAgvfPOO65BcVL5B+IVVxZPwVA63ahQsDuQU1GPl5an+nOWpai69VTW/BdBRf3OcH5G84fq0n4mCnJ+JjIzM7V69eoit5U8fyZQuRCOEXA6duyoTz/9VGvWrJHdbi9T/zwn5x+Uq666Sm+88Ya3i1jk8SZPnqwePXp4dd/O/otPPPGEhgwZUuj55OTkcu3XWea77rqrTDNMREZG6tixY0pNTfXYilRSGCmuLGlpaR6fdzgcOnr0aKHHFy1apPT0dHXq1EmvvvpqoT/C5Z2RITc31zWDx4QJEwq1XObm5urw4cNl2mdiYqJ27dqlxo0ba/z48YVmGPD27BHO97So+nDeFSgvwzBKDD1nqqRzkDyfh6+///ldd911GjdunL799ls99thjOnbsmBYuXKjw8PByT59XFtWqVVNmZmaR9VCwpdlf8of+I0eOqH79+oVe4/yO5Q/0Z/qZ6Ny5s1sfZsATBuQh4PTp00eRkZE6fPiwqy9vWTlvx23dutWbRSuS87ZgaVqOy8rZKuZpIE1OTo62bdvmcbuiWpacyvseOadJ2r59u8fniyrPmexz165dHltonXcXOnbs6PF8i+q/W9J7k5qaquzsbNWqVcvjLf2tW7e6+nyXlrOsbdu2LRSMiytreVVEPUnFh5Njx44VeYFTHs5zcN5KLygrK8vjxaGvv//5xcbGqkePHjp8+LB+//13fffdd8rJyVG/fv3cBppWFOd7VtSczBXxO6o8atas6Wr9Leqz6JzCMf/UbM5pJXfs2OFxGj+Hw+Hx8+L8TGzfvl0Oh+OMyo7QRzhGwImOjtYtt9wiKW+e0v3795d5H127dlVMTIw2b96sZcuWebuIhTgHzMycOdPrt+Sc3Sc8tYbMmTOnyBYU52wXnrpxSHkXIeHh4Vq0aJFbn76S9OzZU1Je/2pPytMq06tXL0nSDz/84DFcFdXf2nmOnlpx09LS9MUXX3jczvmeFvXeOJ/PzMz0+JqPP/7Y43bFce7TU1lzcnJc8/F6i/M9/eKLLzxeWJTUh70ozoU9kpKSCj3n7VH+znNYsWKFx7muZ82a5fHcfP39L+j666+XlDdDhXOWivJ0qSgP5/fTedyC5syZ45NylIazfj0NtjUMQ//73//cXidJXbp0UbVq1bRv375Cs19I0i+//OKxz3Dz5s0VFxeno0ePurq5AEUhHCMg3X///erUqZMOHTqkwYMH64svvih0OzAnJ0c//PCDx1aCqlWr6oEHHpAkPfjgg5o/f36hVoYtW7ZozJgxWrVq1RmXd8CAAerYsaO2b9+uu+66yzUoxunUqVNauHChnnrqqTLvu0uXLpLypiHKH4QXLVqk119/3W3Kt/ycA3nWrFnjsR9rgwYNdNtttyknJ0ejRo0qFCIMw1BiYqKee+45t5kQ/vGPfygyMlLr1q3T22+/7dp3Tk6OXnvttWIX7CjKBRdcoDZt2uj48eP65z//6TYobd68eZoxY4bHWUCcM2j88MMP+uOPP1yPHzp0SA888ECRrbu1a9dW9erVdeTIEY+tVjVr1lSrVq2Um5url19+2TWThN1u14cffqh58+Z5nAGiOB06dFBYWJhWr17t9sf52LFjeuyxx8rcTaMkV155pRo0aKDk5GQ9++yzrpBvGIY++eSTQlOAlZZzhoC3337brcyLFi3Su+++67GeyqtZs2bq37+/DMPQE0884dZKvGzZMo0fP95jPfj6+1/QxRdfrFq1aunnn3/Whg0bVK9ePZ9NnTdkyBBVq1ZNixcv1rhx41zfgdzcXP33v/8tsb+tL40cOVJhYWH6+eefNWnSJFeL7qlTp/TSSy9py5YtqlGjhtsAuqioKNeMJ88//7zb93fz5s168cUXi/xuPvbYY7JYLHrhhRc0a9asQr8X9+zZo/fee08//fSTt08VQYY+xwhIVapU0aRJk/Svf/1L33//vf7973/rP//5j5o0aaKoqCgdPXpUKSkprsEnvXr1KrSy1tChQ3XgwAF9+OGHuu+++1SrVi01adJEDodD+/btc/VhLbhdeVitVo0bN0533nmn/vjjD11yySVq1qyZatWqpaysLFe3gPIMgho9erTmzp2rdevWqW/fvmrRooUyMjK0b98+devWTfXr1/c4r2qvXr0UHR2tVatW6aKLLlKTJk0UFhamCy+80LVi3MMPP6xDhw7pm2++0bBhw1SvXj01bNhQp06d0p49e1wXJMOGDXPtNzY2Vs8//7z++c9/6r333tNnn32ms846S3v27FFGRoYefvhhvfnmm2U6R4vFotdff1233HKLFi1apN69e7tWyNu3b5+GDh2q3377rdAgzXbt2unSSy/Vjz/+qBEjRqhZs2aKjIzU1q1bVbVqVT366KN6+eWXPR7vsssu0+zZszVo0CC1atXK1V3A2Yr1yCOP6J577tHMmTP1448/6qyzztK+ffuUlpame+65R19//XWRg0Y9qVevnoYNG6ZJkybpiSee0DvvvKOYmBht27ZNdrvd9Rn3lsjISL3++uu6/fbbXSvCtWjRQsnJyUpJSdHjjz+uMWPGlHm/o0aN0tdff61Nmzapb9++Ouecc1yfxzvuuENz584t0/tSkueee06bN2/W+vXrdfHFF6tVq1bKzs7Wzp07ddFFFykrK8vj1Fu+/P4XVKVKFV111VWuz1JZ5zY+E40aNdJzzz2np556SuPHj9f06dPVuHFj7d27V+np6Xr00Uc1ZsyYIgdy+lLr1q3173//Wy+88IJee+01TZw4UQ0bNtSuXbuUkZGhKlWq6I033ii0hP1DDz2kVatWacOGDbryyitdM4Bs3bpVbdq0UefOnV1T5+XXp08fPfPMM3rppZf09NNP65VXXlHz5s1lsViUnJzsutjz5vcQwcn/3w6gCJGRkXr77bf1+eefa8iQIWrWrJlSUlK0ceNGZWRkKC4uTiNHjtScOXM0ceJEj4uGPProo5oxY4YGDhyoatWqafPmzdq3b58aNGig66+/Xh9++KHbzBdnon79+po5c6aee+45nXfeeTp69Kg2btyorKwstW/fXvfff3+5bp03atRIn332mS655BKFh4dr+/btqlq1qu6//359/PHHRbbURUVFaeLEierdu7dycnK0du1aLV++3K0PalhYmMaMGaMPP/zQtVT3pk2blJKSoubNm+uWW27xuHz01VdfrU8++UTdunXTyZMntX37dsXFxemjjz7SFVdcUeZzlKRWrVrpiy++0MCBAxUREaGtW7eqevXqeuaZZ/Tss88Wud0bb7yhe+65R40bN9b+/ft1+PBhXXrppfriiy9cU2l58u9//1vDhg1T3bp19ddff2n58uVu87/269dPH330kTp16qQTJ05ox44datasmcaMGeOac7Ws/vnPf+pf//qXzj77bKWkpGj//v264IIL9Omnn1ZIy2L37t31+eefq2/fvrJYLNq2bZtiY2P11ltvuRaRKKvatWtrxowZuuyyy1StWjXt2LFD0dHReuWVV/Too496+Qzy7nB88cUXGjJkiGrVquW6M/HAAw9o/PjxxfYf9+X3v6D83Sh81aXCadCgQZo0aZLOP/98nThxQtu3b1erVq308ccfuxaROdNZK7xl6NCh+vTTT3XxxRfL4XBo8+bNioiI0NVXX60vv/yy0NLRUl7Zp02bpttvv12NGjXSjh07lJWVpeHDh2vatGke+/Q73Xzzzfrqq6904403qnbt2vr777+1a9cuxcTEaODAgXrnnXc8znuNysVieOrRDgAAym3RokW6/fbb1a5dO82ePdvfxXH58ccfXav/TZgwwd/FAQISLccAAHiZczCor1uNS+IckJd/ISUA7uhzDACAF61bt04LFixQVFSUrr76ap8f/8cff1RERIR69erl6ut8/PhxjRs3TgsXLlRkZGS5lscGKgvCMQAAXvDwww9r37592rhxo+x2u+644w6PS35XtC1btmj8+PGqWrWqmjZtqipVqmjbtm06ceKEbDabnn/++UKD3ACcRjgGAMAL1q1bp/379ys2NlY33HCDbr/9dr+Uo3///kpOTtbKlSt14MABnTx5UjExMerXr59GjBih9u3b+6VcQLBgQB4AAABgYkAeAAAAYCIcAwAAAKaQ7HOclpbm82NGR0e7LXmL0EC9hibqNTRRr6GJeg1N/qrXmJiYEl9Dy7GXBMJSnPA+6jU0Ua+hiXoNTdRraArkeg3ckgEAAAA+RjgGAAAATIRjAAAAwEQ4BgAAAEyEYwAAAMBEOAYAAABMhGMAAADARDgGAAAATIRjAAAAwEQ4BgAAAEyEYwAAAMBEOAYAAABMhGMAAADARDgGAAAATIRjAAAAwEQ4BgAAAEyEYwAAEDCuvfZaXXvttRW2/++++07du3fXd999d8b7quiywj8IxwAAAH5y9913q3v37v4uBvIhHAMAAAAmwjEAAB5MnOzQlKmGx+emTDU0cbLDxyUC4Ath/i4AAACByGaz6ONJeeF4+DCL6/EpUw19PMnQ6JGWojb1mV9++UWzZs3Szp07lZWVpVq1aunss8/WoEGD1KdPH9frvv32Wy1atEhbt25VamqqIiIi1Lp1aw0bNkxdunRx2+eqVat07733atSoUerWrZvef/99bd68WVWqVFG/fv30wAMPKCIiQn/++acmTZqkrVu3qlq1arryyit19913y2azufb13Xff6cUXX9TTTz+tqKgoffLJJ9q+fbuqV6+uPn366O6771bNmjVLda6GYei7777TN998o23btslut6tFixa6/vrrddVVVxV6fXp6ut5//30tXLhQ2dnZOvvss3XbbbeV631etGiRJk+erO3btysyMlIXXnih7rvvPo+v3b17t77++mutWLFCycnJOnHihBo0aKCLLrpII0aMUGRkpOu1+btT5P/3FVdcoWeffVZS2eoO3kE4BgDAA2cgzh+Q8wfj/IHZH2bPnq0xY8aobt266tOnj6Kjo3X48GFt3LhRv/32m1s4fuONN9SyZUudd955iomJUUpKin777Tfdf//9evXVV9W7d+9C+9+wYYP+97//qVu3brr22mu1atUqzZkzR1lZWerdu7deeOEFXXjhhWrbtq3++OMP/e9//1P16tU1YsSIQvv69ddftXz5cvXr10/nnXee1qxZoy+//FLr16/XRx99pIiIiGLP1TAMPffcc/rpp5/UtGlTXXrppQoLC9Py5cv10ksvaceOHXrggQdcrz9x4oTuuecebdu2TQkJCerUqZMOHjyop59+Wt26dSvT+zxv3jy98MILql69ui677DJFRUVpyZIluv/++5Wbm6uwMPcotXDhQn377bfq0qWLOnfuLMMwtH79ek2bNk1r1qzR+++/79pm1KhRmjt3rpKTkzVq1CjXPuLi4lz/Lk/d4cwQjoF8Jk52yGbz/EdvylRDdruhUSPojQRUFvkD8ifTDOXkKCCCsSR98803Cg8P17Rp0xQTE+P2XHp6utvPM2bMUKNGjdweO3z4sEaMGKFx48Z5DFhLly7V66+/7nouNzdXw4cP108//aRly5bpvffeU5s2bSRJt99+u2644QZ99tlnuvXWWwsFxiVLlmjcuHE677zzXI+9+OKL+u677zR9+nSNHDmy2HP9+uuv9dNPP+mqq67SE0884dp/Tk6OnnrqKU2fPl2XXHKJzj33XEnStGnTtG3bNl1zzTV66qmnXPu54oor9OCDDxZ7rPyysrL05ptvqlq1apo8ebKaNm0qKW8Q3f3336+//vpLsbGxbttcdtll+sc//qHw8HC3xydOnKiPPvpICxYs0GWXXeZ631avXq3k5GTdfvvtHstQnrrDmeGvPJCP8zZqwX6GztYim83/fxAB+NbwYRaFh0s5OVJ4uAIiGDuFhYUVCqKSFB0d7fZzwXAlSXXr1tVFF12kPXv26MCBA4We79y5s1vwCgsLU79+/WQYhnr16uUKxpJUvXp19erVS+np6Tp06FChfZ1//vluwViS7rzzToWFhWnevHklnucXX3yhatWq6bHHHnM73/DwcN11112SpJ9++sn1+Pfff6/w8HDdcccdbvvp1q2bunbtWuLxnH777TdlZWVp4MCBrmAs5b0Xd955p8dt6tevXygYS9INN9wgSVqxYkWpjy+Vr+5wZmg5BvIpeBv14QcVULdRAfjelKmGKxjn5OT9HAi/C/r3768JEyZo6NChGjBggDp37qwOHTqoRo0ahV67b98+ffLJJ1q1apVSUlJ06tQpt+cPHz6shg0buj2W/9a+U506dSRJrVq1KvK5lJSUQoGuY8eOhV5fr149NW7cWLt27VJWVpaqV6/u8TyPHz+ubdu2qW7dupo6dWqh53NzcyVJu3btkpTX2rt//361aNHCVaaCZVm5cqXHYxW0devWIsufkJDg1r/aydk3eu7cudq+fbsyMzPlcJwevHn48OFSHdupPHWHM0M4Bgpwv416JKBuowLwrYIXx86fJf+3IN96662Kjo7Wl19+qRkzZmj69Omy2Wzq0aOHHn74YVdA3bNnj0aNGqWsrCx17txZvXr1UvXq1WWxWLR69WqtWbOmUOCS5DGsOsNgcc85w2p+Bbt9ONWuXbvEcJyRkSHDMJSSkqKJEycW8W7khWgpLxyXdMzSyszMLHJfNputUAu9JL355pv64osv1KBBA/Xq1Ut169Z1tSRPnDjR43tdlPLWHc4M4RjwYPgwi6t/YaDdRgXgG57uGnkapOcvFotF11xzja655hqlp6dr7dq1+umnn/Tzzz9rz549+vTTT2Wz2fTZZ58pIyND//nPf1x9XZ1ee+01rVmzpsLLmpaW5vHx1NRUSZ7DtpPzuXPPPVdTpkwp8VjO15d0zNKIiooqcl92u13p6emqV6+e275nz56tli1b6uOPP3YbaHjkyJFiw70ngVB3lRF9jgEPPN1GBVC52O2eu1MNH2bR6JEW2e2B83shOjpaffr00UsvvaSuXbtq586d2rt3r6S82/KSdOGFF7pt43A4lJiY6JPyrV27ttBjKSkp2rdvn84666xiw3FUVJSaN2+unTt36tixYyUeq3r16mrUqJH27t2rI0eOlKosRXF2H/G0TVJSkux2u9tj+/fvl2EYOu+88wrNwFHUcZ0t7gX3JQVG3VVGhGOggPytRWtX1tHokZ4H6QEIbaNGWItsGR4+zOL3mWuWLl1aqAtDbm6uMjIyJElVq1aVJNdsCuvWrXN7rXNGB19Yvnx5oYFoH3zwgXJzc3XFFVeUuP3gwYN14sQJvfLKK67uE/nt379f+/fvd/18+eWXKycnRx9++KHb65YtW1bq/saS1Lt3b1WvXl3fffeddu/e7Xo8NzdXH3zwQaHXO9/rpKQkt37Ghw4d0oQJEzwewznPs6eBjIFQd5UR3SqAfAL9NioAOD399NOKiIhQhw4dFBsbq9zcXC1fvlw7duzQxRdf7ApWgwYN0nfffaennnpK/fv3V3R0tNavX68tW7aoZ8+eWrJkSYWXtWfPnnrkkUfUr18/NWjQQGvWrFFSUpJatWqloUOHlrj9oEGDtH79es2bN0+JiYk677zzVLduXaWmpmrXrl3asGGDXnjhBVc/61tuuUULFy7U119/re3bt7vmOf7555/LdM5RUVF65JFH9H//938aMWKEBgwYoOrVq2vJkiWqWrWq6tat6/b6unXrqm/fvvr11181fPhwnXfeeUpNTdWSJUvUpUsXV0twfl26dNEvv/yif//737rgggtUtWpVnXPOOerZs2dA1F1lRDgG8inuNqrzeYlwDMD/7r77bi1dulQbNmzQ4sWLFRERobPOOktPPvmkBg4c6HpdfHy83nnnHX3wwQdauHChbDabEhIS9MEHH+j333/3ScDq27evrrrqKk2ZMkULFy5UZGSkBg0apLvuuqvEBUCkvP7Vzz77rHr06KGvv/5aS5YsUXZ2tmJiYtSkSRPdf//9blPFVatWTRMmTNB7772n3377TVu2bFGLFi304osvKjMzs0znfOWVVyoqKkqTJ0/WvHnzVL16ddcKecOGDSv0+meeeUYNGzbUr7/+qlmzZqlBgwYaMmSIhg0bpl69ehV6/TXXXKMDBw5owYIFmjJliux2u6644gr17NkzIOquMrIYhhFy94qL6oRfkWJiYvxyXFQs6jU0Ua+hiXoNPPmXj84f2MuCeg1N/qrXomYxyY8+xwAAAICJcAwAAACYCMcAAACAiQF5AACgQgwcOLDcfY0Bf6HlGAAAADARjgEAAAAT4RgAAAAwEY4BAAAAE+EYAAAAMBGOAQAAABPhGAAAADARjgEAAAAT4RgAAAAwEY4BAAACyLXXXqtrr73W38Vw6d69u+6++263xz766CN1795dq1at8lOpKg7hGACAILRq1Sp1795dH330kb+LAoSUMH8XAAAAAKeNHz/e30Uo0Y033qgBAwYoNjbW30XxOsIxAABAADnrrLP8XYQS1apVS7Vq1fJ3MSoE4RgAgCDz0UcfaeLEiZKkiRMnuv4tSXPmzFGjRo30wgsvaN68eZo9e7YWLVqkb775Rnv37tWAAQP07LPPup53vt7T/t9991116dLF7bk1a9bof//7n9avX6/s7Gw1aNBAF198sYYPH66IiIgSy75//35dd911uuKKKzRs2DC99957Wrt2rdLT093KsmjRIn3++efasmWLTpw4obPOOktXXnmlhgwZIpvN5rbPEydO6KOPPtL8+fN19OhRnXXWWRo8eLCaNGmie++9V6NGjdLtt9/uen337t3VqVMnPf/883r//fe1dOlSpaWlafz48a7zLct5/vLLL5o1a5Z27typrKws1apVS2effbYGDRqkPn36uF63atUqTZs2TX///bfS09MVHR2tJk2a6LLLLtM111zjep2zv/FXX31V6DynTZumBQsW6MCBA4qIiFC7du00fPhwtW/fvsg6TEtL09SpU7Vr1y5FRUWpX79+uvfee0tVX0Xx9BnJX7ejRo3S+PHjtXLlSuXk5Khdu3Z68MEH1apVq0L7Sk1N1dSpU7V48WIdPHhQkZGR6tSpk26//Xadc8455S5jeRGOAQAIMp07d9aBAwc0b948derUSZ07d3Y9V6NGDbfXvvnmm1q/fr169uypnj17qnbt2uU+7pw5czRmzBjVqFFDvXr1UkxMjDZu3KgpU6Zo1apVmjBhgsLDw0u1r71792r06NFq0aKFrrjiCmVkZLi2fe+99/TJJ5+ofv36uuSSSxQWFqa1a9dq3Lhx2rBhg15++WXXfux2ux599FGtWrVKrVq10iWXXKKMjAyNHTvW7X0pKCMjQ7fffrtq1qypiy++WDk5OapevXqZz3P27NkaM2aM6tatqz59+ig6OlqHDx/Wxo0b9dtvv7nC8ZIlS/TYY4+pRo0auvDCC1W3bl2lpaVp69at+vHHH93CsSenTp3Sfffdp/Xr1ys+Pl433XST0tLStGDBAi1btkwvvvii+vbtW2i72bNn688//9SFF16ozp07a+nSpZo1a5bS09P1wgsvlKquyurAgQMaNWqUWrRooYEDB2rfvn1atGiR7r33Xs2YMUN16tRxvXbv3r265557lJKSom7duql3795KS0vTr7/+qmXLlmncuHFq165dhZSzKIRjAEDIsW35QVX/GCedyvJ3UTyrUl0nezwge9yl5drc2VI3b948de7c2a1VtKC///5bU6dOPeO+oTt27NCbb76pVq1aady4cYqOjnY9N3XqVE2YMEGff/65br755lLtLzExUSNHjtQdd9zh9viyZcv0ySef6IILLtArr7yihg0bKi0tTYZh6PXXX9eXX36pX375Rf369ZMkzZ07V6tWrdKFF16o1157TVZr3lwDQ4cO1W233Vbk8bdt26aBAwfqqaeecmuJLut5fvPNNwoPD9e0adMUExPjdoz09HTXv7/99lsZhqF33323UOtp/tcVxdmKfemll+o///mPLBaLJOmmm27SqFGj9Morr+j88893BXyn5cuXa8qUKWrWrJmkvNbnYcOGaf78+br//vtVr169Eo9dVmvWrNE999yjYcOGuR774IMPNHnyZM2dO9ft8eeff15HjhzR22+/rW7durkeHzFihIYPH65XXnlFn376qdfLWBxmqwAAhJwqKybJmrpd1syDgflf6nZVWTnJJ+/FzTff7JVBU19++aXsdrseeeQRt8AoSbfccotiYmI0f/78Uu+vTp06GjFiRKHHv/jiC0nSk08+6Xbb32Kx6N5775XFYnE7zg8//CBJuuOOO1zBWJKaN2+uK664osjjh4eH67777ivURaM85xkWFqawsMLtjQW3l6SqVauW6nUFzZ07V2FhYa73wKlVq1a68sorlZGRoUWLFhXa7qabbnIFY0mKiIjQgAEDZBiGNm/eXOJxy6NRo0a65ZZb3B676qqrJEkbN250PfbXX38pKSlJV1xxhVswlqSmTZvqmmuu0bZt27Rt27YKKWdRaDkGAIScU+eNUtU/xgZ0y/GpriN9cqi2bdt6ZT/r16+XJC1dulQrVqwo9HxYWJh27dpV6v21atXKYxeM9evXq1q1avrmm28kSdWqVdPx48ddz1etWtXtOH///beqVavmsS9rQkKCvvzyS4/Hb9SokccBZWU9z/79+2vChAkaOnSoBgwYoM6dO6tDhw6Furf0799fCxcu1OjRozVgwAB16dJFHTt2LFU3l6ysLO3bt0/NmzdX/fr1Cz3fuXNnffnll9q6dasuv/xyt+fi4+MLvd65j8zMzBKPXR6tWrVyu1Ap6pjO9zo1NdXjlITO93nXrl0+7XtMOAYAhBx73KXKLmeXhVBzJn2M88vIyJAkTZkyxSv7K6pcGRkZstvtboMMC8oflrOysjwGxuKOUdLxpdKf56233qro6Gh9+eWXmjFjhqZPny6bzaYePXro4Ycfdg0wHDBggMLCwjRz5kx99dVXmj17tiwWizp37qwHH3xQcXFxRR4jKyur2DI7H/cUdgt2s5Dkai232+2lOsey8nRMZ8t6/mM63+slS5ZoyZIlRe4vf337AuEYAIBKyNmy5ykgOcNYfs7A8/PPP3sMP95SvXp1WSwW/fjjj5KkmJgYpaWlFfv6o0ePenwuNTW1XMeXSn+eFotF11xzja655hqlp6dr7dq1+umnn/Tzzz9rz549+vTTT11htG/fvurbt6+ysrKUmJiohQsX6ttvv9WDDz6ozz//vFBrc8EyFXU+zscrsl4qgrO8jz76qG688UY/l+Y0+hwDABCEnIHL4XCUa3tnEEtJSSn03F9//VXoMWf3DOet8IrStm1bpaena/fu3aV6fcuWLXX8+HFt3bq10HNJSUnlOr5UvvOMjo5Wnz599NJLL6lr167auXOn9u7dW+h11atX1wUXXKCnnnpKV155pdLS0rRhw4Yi91u9enU1btxYe/fu1aFDhwo9v2bNGkkqtvU5EDnf6/LUU0UiHAMAEIRq1qwpSR7DUmm0bt1aUt5Ar/x++eUXV9jK7/rrr5fNZtNbb72lgwcPFnr+2LFjHkN1WQ0ePFiS9NJLL3mcxeHIkSPasWOH6+dLL83rPvPhhx+6XSjs3LlT8+bNK/Pxy3qeS5cuVW5urttrcnNzXV0GnAPwVqxYoZMnTxban7PV19NAvfyuuOIK5ebm6r333pNhGK7Ht23bprlz5yoqKkq9e/cu5VkGhrZt26pt27aaP3++x8GcDodDq1ev9nm56FYBAEAQatasmerVq6cFCxYoIiJC9evXl8Vi0XXXXaeoqKgSt+/du7caNWqkuXPn6uDBg4qPj9fOnTu1cuVK9ejRQ3/88Yfb68855xw9/vjjGjNmjAYPHqwePXqocePGysrK0v79+7VmzRpdeeWVeuKJJ87ovC644AKNHDlSkyZN0g033KDevXurdu3aSk9P1969e7Vu3TrdeeedatGihSRp4MCB+uGHH/T7779r+PDh6tatmzIyMjR//nydd955Wrx4caHBYcUp63k+/fTTioiIUIcOHRQbG6vc3FwtX75cO3bs0MUXX+yaKWTs2LE6ePCgOnXqpIYNG8pisWjdunXauHGjEhISCi3iUdAtt9yiJUuW6Pvvv9fOnTvVtWtXHT16VAsWLFBubq6effbZoOtWIUn/93//p3vuuUfPPPOMZs6cqXPPPVdVqlTRwYMHlZSUpKNHj3qchaMiEY4BAAhCNptNr7zyit599119//33ys7OliRdfPHFpQrHERERGj9+vN5++22tXLlSGzZsUNu2bfX+++9r8eLFhcKxlLdyW1xcnGbMmKG1a9fq999/V1RUlBo0aKAhQ4YUO3VaWdxxxx3q2LGjPv/8c/3555/KyMhQdHS0GjVqpFGjRrlai53vw1tvveVaIW/mzJlq3LixHnjgAdWsWVOLFy8uc2gsy3nefffdWrp0qTZs2KDFixcrIiJCZ511lp588kkNHDjQ9bphw4Zp4cKF+uuvv7Rs2TKFhYWpUaNGuu+++1yt1cWpWrWq3n33XdcKeZ999pkiIiLUsWNH3XbbberYsWOZzjFQNGrUSFOnTtWMGTO0aNEiffvtt7LZbKpTp446duzoms/alyxG/rb5EFFcx/2KUtKAAQQn6jU0Ua+hiXoNTWdSr++//76mTJmit956Sz169PByyXAm/PV9LbhQiyf0OQYAAEHt8OHDhR7bsWOHawaI4paRBgqiWwUAAAhqr7/+ug4cOKA2bdqoRo0a2rdvnxYvXqzc3Fz9+9//dltpDygJ4RgAAAS1fv366csvv9TChQuVmZmpyMhIderUSUOHDlX37t39XTwEGcIxAAAIapdddpkuu+wyfxcDIYI+xwAAAICJcAwAAACYCMcAAACAiXAMAAAAmAjHAAAAgIlwDAAAAJgIxwAAAICJcAwAAACYCMcAAACAiXAMAAAAmAjHAAAAgIlwDAAAAJgIxwAAAICJcAwAAACYCMcAAACAiXAMAAAAmAjHAAAAgCnM3wUoimEYmj9/vqZNm6YdO3bo2LFjio2NVbdu3XT77berSZMm/i4iAAAAQkzAhuPXXntNkydPVr169dS/f39FRUVp8+bN+vzzz/Xdd9/ps88+U1xcnL+LCQAAgBASkOE4JSVFn3zyiRo3bqxvvvlGUVFRruemTJmiV155RZMnT9Yrr7zix1JWHhMnO2SzWTR8mKXQc1OmGrLbDY0aQQ8dAAAQ/AIy0ezbt08Oh0OdO3d2C8aSdNFFF0mSUlNT/VCyyslms+jjSYamTDXcHp8y1dDHkwzZbIVDMwAAQDAKyJbjZs2aKTw8XKtXr1ZmZqZbQP7tt98kSd27d/dX8SodZ4vxx5MM18/OYDx6pOcWZQAAgGAUkOE4JiZGDz/8sF5//XVdccUV6tevn6pXr64tW7bozz//1E033aRbbrnF38WsVPIH5E+mGcrJEcEYAACEHIthGEbJL/OPb7/9Vs8++6yys7Ndj3Xq1EmPPfaYunbtWuR2DodDVmtA9hgJeh27HlFOjhQeLq1dWcffxQEAAPCqgGw5lqQJEyZowoQJuu+++3TttdeqZs2a2rRpk1599VUNGzZMb7/9ti655BKP26anp/u4tHmt3WlpaT4/ri9NmWq4gnFOjvTfd1JDvuW4MtRrZUS9hibqNTRRr6HJX/UaExNT4msCsnn1zz//1DvvvKObb75Zd911l2JjYxUZGakuXbrogw8+UNWqVZmpwsfy9zH+db5Vo0d6HqQHAAAQzAKy5dg56K5bt26Fnqtdu7bi4+O1Zs0apaamqnbt2r4uXqXjafCdp0F6AAAAwS4gw3FOTo6koqdrcz5epUoVn5WpMrPbPc9K4fzZbjckEY4BAEDwC8huFZ07d5aUt+DHsWPH3J778ssvtWvXLrVt27bQHMioGKNGWItsGR4+zMICIAAAIGQEZMvxZZddps8++0zLly/XJZdcon79+qlmzZr666+/tGTJElWpUkX/+te//F1MAAAAhJiADMc2m00TJ07UJ598ou+//15z585VTk6O6tSpo4EDB+rOO+9UXFycv4sJAACAEBOQ4VjK6098++236/bbb/d3UQAAAFBJ0FkUAAAAMBGOAQAAABPhGAAAADARjgEAAAAT4RgAAAAwEY4BAAAAE+EYAAAAMBGOAQAAABPhGAAAADARjgEAAAAT4RgAAAAwEY4BAAAAE+EYAAAAMBGOAQAAABPhGAAAADARjgEAAAAT4RgAAAAwEY4BAAAAE+EYAAAAMBGOAQAAABPhGAAAADARjgEAAAAT4RgAAAAwEY4BAAAAE+EYAAAAMBGOAQAAABPhGAAAADARjgEAAAAT4RgAAAAwEY4BAAAAE+EYAAAAMBGOAQAAABPhGAAAADARjgEAAAAT4RgAAAAwEY4BAAAAE+EYAAAAMBGOAQAAABPhGAAAADARjgEAAAAT4RgAAAAwEY4BAAAAE+EYAAAAMBGOAQAAABPhGAAAADARjgEAAAAT4RgAAAAwEY4BAAAAE+EYAAAAMBGOAQAAABPhGAAAADARjgEAAAAT4RgAAAAwEY4BAAAAE+EYAAAAMBGOAQAAABPhGAAAADARjgEAAAAT4RgAAAAwEY4BAAAAE+EYAAAAMBGOAQAAABPhGAAAADARjgEAAAAT4RgAAAAwEY4BAAAAE+EYAAAAMBGOAQAAABPhGAAAADARjgEAAAAT4RgAAAAwEY4BAAAAE+EYAAAAMBGOAQAAABPhGAAAADARjgEAAAAT4RgAAAAwEY4BAAAAE+EYAAAAMBGOAQAAABPhGAAAADARjgEAAAAT4RgAAAAwEY4BAAAAE+EYAAAAMBGOAQAAABPhGAAAADARjgEAAAAT4RgAAAAwEY4BAAAAE+EYAAAAMBGOAQAAABPhGAAAADARjgEAAAAT4RgAAAAwEY4BAAAAE+EYAAAAMBGOAQAAABPhGAAAADARjgEAAAAT4RgAAAAwEY4BAAAAE+EYAAAAMBGOAQAAABPhGAAAADARjgEAAAAT4RgAAAAwEY4BAAAAE+EYAAAAMBGOAQAAABPhGAAAADCF+bsAJZk/f76mT5+ujRs36vjx46pbt646duyoxx9/XA0bNvR38QAAABBCAjYcG4ah5557TjNnzlTTpk11xRVXqHr16jp06JBWrFihffv2EY4BAADgVQEbjqdNm6aZM2fq5ptv1r///W/ZbDa353Nzc/1UMvjKxMkO2WwWDR9mKfTclKmG7HZDo0bQMwgAAHhPQCaLEydO6N1331WTJk30r3/9q1AwlqSwsIDN9fASm82ijycZmjLVcHt8ylRDH08yZLMVDs0AAABnIiAT5pIlS3T06FENGjRIDodDP/30k3bu3KkaNWqoR48eatasmb+LCB9wthh/PMlw/ewMxqNHem5RBgAAOBMBGY7Xr18vSbLZbLr66qu1Y8cO13NWq1XDhw/XE0884a/iwYfyB+RPphnKyRHBGAAAVBiLYRhGyS/zrWeffVYzZ86UzWZTmzZt9Oyzz+qcc87Rpk2b9Mwzz2j79u167rnnNHToUI/bOxwOWa0B2WME5dSx6xHl5Ejh4dLalXX8XRwAABCiArLl2JnXw8PD9e6776pBgwaSpK5du2rs2LG6+uqrNXny5CLDcXp6us/K6hQTE6O0tDSfH7cymDLVcAXjnBzpv++k+qzlmHoNTdRraKJeQxP1Gpr8Va8xMTElviYgm1ejoqIkSe3atXMFY6dWrVqpSZMm2r17tzIyMvxRPPhQ/j7Gv863avRIz4P0AAAAvCEgW47PPvtsSVKNGjU8Pu98/MSJE6pZs6bPygXf8jT4ztMgPQAAAG8JyHDcrVs3SdL27dsLPZeTk6Pdu3crMjJStWvX9nXR4EN2u+dZKZw/2+2GJMIxAADwnoAMx02bNlWvXr20ePFizZo1SzfeeKPruQ8//FAZGRm6+uqrmes4xBW3wEdeQCYYAwAA7wrYdPncc89pyJAhevrpp7VgwQKdffbZ2rhxo5YuXarGjRvrn//8p7+LCAAAgBATkAPypLzW49mzZ+u6667Thg0bNG3aNO3atUs333yzZs2apXr16vm7iAAAAAgxAdtyLEkNGzbUK6+84u9iAAAAoJII2JZjAAAAwNcIxwAAAICJcAwAAACYCMcAAACAiXAMAAAAmAjHAAAAgIlwDAAAAJgIxwAAAICJcAwAAACYCMcAAACAiXAMAAAAmAjHAAAAgIlwDAAAAJgIxwAAAICJcAwAAACYCMcAAACAiXAMAAAAmAjHAAAAgIlwDAAAAJgIxwAAAICJcAwAAACYCMcAAACAiXAMAAAAmAjHAAAAgIlwDAAAAJgIxwAAAICJcAwAAACYCMcAAACAiXAMAAAAmAjHAAAAgIlwDAAAAJgIxwAAAICJcAwAAACYCMcAAACAiXAMAAAAmAjHAAAAgIlwDAAAAJgIxwAAAICJcAwAAACYCMcAAACAiXAMAAAAmAjHAAAAgIlwDAAAAJgIxwAAAICJcAwAAACYCMcAAACAiXAMAAAAmAjHAAAAgIlwDAAAAJgIxwAAAICJcAwAAACYCMcAAACAiXAMAAAAmAjHAAAAgIlwDAAAAJgIxwAAAICJcAwAAACYCMcAAACAiXAMAAAAmAjHAAAAgIlwDAAAAJgIxwAAAICJcAwAAACYCMcAAACAiXAMAAAAmAjHAAAAgIlwDAAAAJgIxwAAAICJcAwAAACYCMcAAACAiXAMAAAAmAjHAAAAgIlwDAAAAJgIxwAAAICJcAwAAACYCMcAAACAiXAMAAAAmAjHAAAAgKnc4fj999/XoUOHvFkWAAAAwK/KHY7ffvtt9evXT/fee69+++03GYbhzXIBAAAAPlfucHzfffepfv36+vnnn3XXXXfpoosu0rhx47R//35vlg8AAADwGYtxBk2+hmHo999/1xdffKFffvlFubm5slqt6tmzpwYPHqx+/frJZrN5s7ylkpaW5vNjxsTE+OW4qFjUa2iiXkMT9RqaqNfQ5K96jYmJKfE1YWdyAIvFot69e6t3795KTU3V7Nmz9cUXX+j333/X4sWLVbt2bV133XW64YYb1KxZszM5FAAAAFDhzqjluCgrVqzQjBkzNG/ePFksFknS+eefr1tuuUUDBgzw9uEKoeUY3kK9hibqNTRRr6GJeg1Ngdxy7PWp3Pbs2aPFixdr5cqVkvK6XtSrV0/Lli3TAw88oBtvvFHJycnePiwAAABwxs6oW4VTTk6O5s+fr1mzZmnZsmVyOByKjo7WsGHDdNNNN+mcc87R6tWr9cEHH+i3337T//3f/+ndd9/1xqEBAAAArzmjcLxt2zbNmjVLX3/9tY4ePSrDMNSxY0cNGTJEl19+uapWrep6befOnfXBBx9o8ODBWrZs2RkXHAAAAPC2cofjoUOHas2aNTIMQ1FRURoyZIiGDBmi+Pj4Yrdr2bKlkpKSyntYAAAAoMKUOxyvXr1abdu21ZAhQzRw4EBVq1atVNvdeOONOu+888p7WAAAAKDClDscz5o1SwkJCWXerlOnTurUqVN5DwsAAABUmHLPVlGeYAwAAAAEMq9P5QYAAAAEK8IxAAAAYCIcAwAAACbCMQAAAGAiHAMAAAAmwjEAAABgIhwDAAAAJsIxAAAAYCIcAwAAACbCMQAAAGAiHAMAAAAmwjEAAABgIhwDAAAAJsIxAAAAYCIcAwAAACbCMQAAAGAiHAMAAAAmwjEAAABgIhwDAAAApqAJxx999JHi4+MVHx+vtWvX+rs4AAAACEFBEY63bdumsWPHKjIy0t9FAQAAQAgL+HBst9v1xBNP6Nxzz9XFF1/s7+IAAAAghAV8OP7oo4+0efNmvfzyy7LZbP4uDgAAAEJYQIfjLVu2aPz48br77rvVqlUrfxcHAAAAIS5gw3Fubq6efPJJnXPOObrjjjv8XRwAAABUAmH+LkBR3n//ff3111/6/PPPFR4eXqZto6OjZbX6PvfHxMT4/JioeNRraKJeQxP1Gpqo19AUqPUakOF48+bNev/99zVy5Ei1bdu2zNunp6dXQKmKFxMTo7S0NJ8fFxWLeg1N1Gtool5DE/UamvxVr6UJ5AHZreKJJ55QkyZNdP/99/u7KAAAAKhEArblWJISEhI8Pn/TTTdJkt59912mdwMAAIDXBGQ4vuGGGzw+vnLlSu3cuVP9+vVT7dq11bhxYx+XDAAAAKEsIMPxSy+95PHxJ598Ujt37tSdd96pjh07+rZQAAAACHkB2ecYAAAA8AfCMQAAAGAKqnD86quv6q+//qJLBQAAACpEUIVjAAAAoCIRjgEAAMpg4mSHpkw1PD43ZaqhiZMdPi4RvIlwDAAAUAY2m0UfTzIKBeQpUw19PMmQzWbxU8ngDQE5lRsAAECgGj4sL/x+PMlw/ewMxqNHWlzPIzgRjgEAAMoof0D+ZJqhnBwRjEME3SoAAADKYfgwi8LDpZwcKTxcBOMQQTgGAAAohylTDVcwzslRkYP0EFwIxwAAAGWUv4/xr/OtGj3S8yA9BB/6HAMAAJSBp8F3ngbpITgRjgEAAMrAbvc8K4XzZ7vdkEQ4DlaEYwAAgDIYNaLoXql5AZlgHMzocwwAAACYCMcAAACAiXAMAAAAmAjHAAAAgIlwDAAAAJgIxwAAAICJcAwAAACYCMcAAACAiXAMAAAAmAjHAABUUhMnOzRlquHxuSlTDU2c7PBxiQD/IxwDAFBJ2WwWfTzJKBSQp0w19PEkQzYbyyCj8gnzdwEAAIB/DB+WF34/nmS4fnYG49EjLa7ngcqEcAwAQCWWPyB/Ms1QTo4IxqjU6FYBAEAlN3yYReHhUk6OFB4ugjEqNcIxAACV3JSphisY5+SoyEF6KB4DHEMD4RgAgEosfx/jX+dbNXqk50F6KJk/BjgSyL2PPscAAFRSngbfeRqkh9LxxwBHZyDPf3zJvW5RNoRjAAAqKbvdc2hz/my3G5IIV2Xh6wGOzDjifRbDMELuvklaWprPjxkTE+OX46JiUa+hiXoNTdRraArWeu07wOHqx/3r/IrvxeoMxM5+44EejP1VrzExMSW+hj7HAAAAXuSPAY7MOOI9hGMAAAAv8dcAR2Yc8R76HAMAAHiBvwY4Fjyu8+eKOl6oIxwDAAB4gbcGOE6c7JDN5rnP8JSphux2Q6NGWF0/M+OIdxGOAQAAvMAZWD3JC6ilC6llmZ6NGUe8j3AMAADgQVlacL2puOnZunR2D8z5W5ALlqcsgRynMSAPAADAA3+seOc0fJjFNZiv7wCHKxivWl14sJ0vylOZ0HIMAADggb8X2Bg+zOJaSCQ8XHrnLWuhwXYs+OF9hGMAAIAi+HrFu/w8Tc/mz/JUFnSrAAAAKIY/Ftgobr5kFvyoWIRjAACAYvh6gY2ipmdzBuQHH3Gw4EcFIhwDAAAUwR8r3hU3PZtzUJ6vV+CrTOhzDAAA4IG/Ftgoanq4KVMNVzBmwY+KQzgGAAAVwl/zBHtLoC2wEWjlCVWEYwAAUCHKstJbIPLWinfeEmjlCVWEYwAAUCH8PU8wUB6EYwBASHj3vWydOmUE7S38UMW8vAg2/JYAAIQEq1V+W+oXxWNeXgQTwjEAICTcfWdkoWmtuIUfGHw9TzBwJuhWAQAIGdzCDzwFL1CcP0u0ICMwEY4BACFl+DCLKxhzC9+//DVPMHAmCMcAgJDi6RY+Acw/mJcXwYhwDAAIGdzCDyzMywuXk5myHdwga3KibMlJyo2sIfV8TKoW4++SFUI4BgCEhPc+yOYWPooV7Cv2BYOJkx0Kt+Zq+OV/y3ogLwhbkxNlPbJNFp0eiGlICq91jnK6jgy4955wDAAICQ6H58F33MKHU7Cv2BeQDEOWjH2yHVgna3KSBh9LVMzJjYr438nit6t1luzNewXke084BgCEhHvvjlRamuc/yNzCh8SKfV5x/KirNdhmdpGwHE9zPd1Qkmzum9gVps1H43UorJ1+2dpe5/Ztr9se7qJJ444G5HtPOAYAAJUG0/155rHLSe5JWQ9t0spvE1U/J1FxkUmyHt1d4r4c0U219USCvl6ZoM2ZCVp/pLWGDY/Q8GEWbZhqaMwkQ2/PSAvY955wDAAAKhWm+yvMZjW04PPtij+xXn3OMfsKp/wliyNHvZ0vOlV4u+OWWgpv3l6OBgmyN2wve2yCVC1GjSXNGuAo9B4Hw3tPOAYAAJUK0/1JlqwUtwFz92au1339jkmZktZ53sawVZWjfmvZG7bXr1sTNPbLBF1+UxMNH1R4IF1R73EwvPeEYwAAUGlUyun+TmXJenCDbMlJp2ePOHag2E0chkU7jp2tU/USlBzWXh/MS1Dv6+I07B9V8t6zT4vuK1zUe7xmraFVq/O6Ujz8YG39953UgHzvCccAAKBSqBQr9jlyZT3inEYtUdbkJFmP/C2L4Sh+s+r15IhtL3vDDnrozbZKPNJOpyxR+nW+VU0kbahm6MNJhib/z1FsX+Gi3mNnMO7SWQH/3hOOAQBApRByK/YZhizH9suanCSbMwwf3ChL7vHiNwuPlD02QY7YBPP/HWTUaCApL9z+edAo1O2htH2Fi3qP2ye4/98pEN97wjEAAKgUgn7FvhPpsh1cn6+vcJKs2YeL3cSw2OSoF+caMOeIbS9H7bMlq63Qa4vrciKpVH2Fi3qPg+m9JxwDAAAEmtxTsh7+S7YDia45ha1pO0vczFGzsSsE22Pby1G/tRRercTtStPlpLL00yYcAwCAUmH55QpiGLIc3SnbgbzWYFtyoqwpm2Sx5xS/WdXovG4R5hRqjtgEGZF1ylWEorpDOHXqGPh9hb2FcAwAAEqF5Ze9w5J9JK81+ECiGYaTZDmZUew2hi1cjnqtZW/YwdVX2KjVTLJ45z0v6qIm5PpplwLhGAAAlArLL5dDznFZD2107x6Rsb/EzRwxLfK6Rzj7CteLl2xVfFBgd8HUV9hbCMcAAKDUWH65GA67rKnb3BbXsB7eKothL36zyLp5rcHOvsIN2kkRNX1UaBREOAYAAGUSDEsAVzjDkCUzWdYDeX2E86ZR2yBLTnbxm4VFyNGgreyxHWRvmCBHbHsZNRp6rXsEzhzhGAAAlEkwLAHsdSeP5U2jZs4pbE1OlDUrpdhNDItVjjotzZkj8gbOOeq0lKzEr0BG7QAAgFKrFMsv20/JenirrAfWuZZctqRul0VGsZs5ajR0BWF7bIIcDdpKVar7qNDwFsIxAAAolZBcftkw9MXEXWrkSNJFrfKCsPXQRlnsp4rfrEqUOX1avmnUour7qNCoSIRjAABQKiExrdfxNHOp5STX7BHDT6TnPbfG8yZ2hUkNzs03p3B7GTHNJQtzOociwjEAACiVoJvWK+eErCmb8gbLOQNx+p4SN3NEN9XWEwn6amV7nd2rvS6/rbUUVtUHBUYgIBwDAIDgZzhkSd2e10f4wDpZk5NkPbxFFkdu8ZtVi5Hd7Brx44YEvTmznbJVyzVF3eXB1k0EZ4xwDAAAgo4l85D7KnMHk2Q5lVXsNoatqjmNWoK5ylx7GdFnuaZR63eB9H8zHT6boo7luAMT4RgAAD8jJJXgVJZsyevNPsLm4hqZB4vdxJBFjjrnFJhGrZVkCy9yG19PUeeP5bj5rJWMcAzAL/gFDZzmj5AUsOw5sh7Z6ppPOCdlg6of2lLyNGpRDVytwXmrzLWVqkaV+rD+mKLOH8tx81krGeEYgF/wCxo4zR8hKSAYhiwZ+9wHzB3aKEvuCbeXFTx7IzyywDRq7WXUaFDuYvhzijpfL8ddaT9rZUA4BuAX/IIG3Pk6JPnF8aN5q8yZi2tYk5NkPZ5a/DZWm+x148wg3F72hu1lxLSQrDavFcvfU9T5ejnuSvFZOwMWwzCKv08RhNLS0nx+zJiYGL8cFxWLeq14zkDs7OPni1/Q1GtoCpV67Tvg9ICwX+cHcdei3JOypmw+PWAueZ2sR3eXuJkjuonbgLma8T10NPNEidsFM3/8HpT8+1nz1/c1JiamxNfQcgzAr3zdYgIEMl8PCPMawyFL2k6ze0RS3v9T/pLFkVP8ZhHRZh/hBNd0aoqs7fYaS3g1SaEbjv21HHfQftZ8gHAMwK8q8y9oBiUiP3+FpPKwZKWYrcFmX+GD62U5eazYbQxbFTnqtz49YC42QUatpq5p1EJZUd91Zx136iif9nUOps+aPxCOAfhNZf8FzaBEOPlzQFiJcrJlPbjBbcll67EDJW7mqH22qzXYEdtejnpxkq2KDwoceIr6rq9anfdYl86+6+sc0J+1AEE4BuAX/IJmUCJO8/eAMBeHXdYjf7strmE9slUWw1H8ZtXryhHb4XRf4QbtpIiaFV/eIFHUd33N2qL7F1fUctwB81kLYAzI85JQGQgCd9RrxfFnl4JAq1d/DcapKP6q20Cr14BnGLJkJptTqJmtwgc3yJKTXfxm4ZGuVebsse3laNheRlRshXWPCKV6DbXv+plgQB4AFFBcOKqoFpNAFWqDEukuEqBOZORNo+bsK5ycKGvW4WI3MSxWOerGuS2u4ahzjlenUatMQu27HqoIxwDgZ6E2KJHuIgHAfkrWlC3mcstmq3Dq9hI3c9Rs5DZgztGgjRQe6YMCFy9UBq+G2nc9VBGOAcCPQnVQIosM+JBhyHJ0t2uwnC05UdZDm2Sxnyp+s6o1T/cRbthejgYJMqrX9VGhyyYU7kaE6nc9FBGOAQSFUGk5yi/UByVyC7mCZKeebg02u0hYTqQXu4lhC5ejXmu3xTWMmGaSJTi+M8F+NyLUv+uhhnAMICiEQstRQaE+apxbyF6Qc0LWQxvNPsJmX+H0vSVu5ohp7ppCzR7bXo5650phwT2NWjDfjQj173qoIRwDCAoV3XLkj5bpUB6UyC3kcnDYZU3d7j5gLmWLLIa9+M2q1ZajYft8fYXbSRHRbq/J+3x7vjgJpjsvBe9G2O2Gpkz1/JkKpPMK5e96KCIc+0go3hIGfK0iW45CsWXaX7iFXDqWYwdP9xFOTspbZe5UVrHbGGER5jRq7V19hY0ajUqcRi1UPt8F70YkJp1eSCOYzwuBhXDsI6Hyiwnwt4rqxxrsfRoDCbeQ87g1ipzMlO3gBlcYPrE9UdUdh4rd3rBY5ajT8vQ0ag3by1GnpWQt+5/uUPh8F3U3okvn4D4vBB7CsY+Ewi8mIBBUZD/WYO7TGEgq/S1ke46sh7eo/alEpW9K0sm0RNW2b5dFp9fcivKwmaNGQzMIm32FG7SVqlT3WrGC+fNd0t0IZ0AOtvMKZqF8R5xw7EPB/IsJCAS+6MfKDAsoE8OQJX2v+4C5gxtlsZ9UX0lqKslDl+GTlijZmrQ7PWAuNkFGVP0KL26wfr5LczciMUlBd17BLJTviBOOfSxYfzEB/uarfqzMsBA4ArJl6niabMnr3RbXsBwvfglcu8K0+Wi8NqYnKDE1Qef2ba9rRpytHD9Moxasn++S7kZMmSrl5BhBd17BLJTviBOOfSxYfzEB/uaLfqzMsBBY/N4ylXtS1kObTrcKH0iUNX13iZs5opvmLarh7Ctcv7WGXx7u+t3/xEj/3GoO1c93qJ5XMAjVO+KEYx/iCwyUX0X3Y2WGhcDj05YpwyFL2s68AOycQSLlL1kcucVvVi1GdmcIdk6jVi3G7TV5jSL+bdUM1c93qJ5XMAnFO+KEYx/hC4zyCshbyyGIGRYCU0W1TFkyD+mXTxPV0JGkjvUSZUteL8upzGK3MWxV5WjQxm1xDSP6rGKnUQuURpFQ/XyH6nkFk1C8I0449hG+wCivom4t3/+QQ2vWyuOtZUJz2VX6GRYC2Bm3TJ3KkvXgBtlci2skyXrsgK5yPu+hp4TDsCgt7GzVPPf0gDlH3TjJFl7qwwZSo0iofr5D9by8wRcNK4Fy8edthGMf4QuM8irq1vKatZ5fHwojhYH8ytQy5ciV9cjfsh44vbiG9cjfshiOYo+RZa2nqi3aa8WBBE1akKDzBrbT0OE1dfIMyl2RjSLcUUJJKrrPfiBd/Hkb4RgIAkXdWnY+5nxNqIwURsUKpmBVbMvUrZLl2H6zn3CScg9vUvV962TJPV7sPo3wSNkbtHOtMPfZ4gS980l9hYdbXN+toV74/lRko4jfByueoWD6DAariu6zH8p3xAnHQJAo7tZyqI0URsUKlmBV6A/5iXSN6r1eXbMTdXL9OlnfXq9I44jr9Z7+FBsWmxx141xB2BGbIEftcySrzfWaG1tJE6Y7gmpAUbBPoxUsn8FgV5GzSYTyHXHCMRAkirq1HIojhVGxgiJY5Z5S3ZMb9c4/1qtHvUTZJifJmrZTktRdkmKlfAvOuThqNs4bMNewQ97/67eRwqsVe6hgHVAUzNNoBcVnMETwN6LsCMdAECju1rKkoPzDDv8KqGBlOGQ5uku2A0nmNGpJsqZs0hB7Tt7zm4rYrGq0OXNEO9kbtleN+At1NKdsf9aCfUBRMAcfT5/BTh2Lfj3dLconWC/+/IlwDAS40gx6CNY/7PAvXwcrZz/TETek5oXgA84ll5NkOZlR7LaGLVyOeq1dM0fYG7aXUauZ2zRqlqgYKa341eryC4UBRcEefAp+Brt0pruFNwX7xZ+/EI6BAFfUoAenTh0VtH/Y/WHiZIeqV8/WkMGFn6tsLVM+CVY5x13TqF2RlajqRxNV/f39JW7miGlhdo8wp1KrGy+FVfFq0YJ9QFEoBJ+Cn0Ep72I//3m890E23S3KIRQu/vyFcAwEuKKCWrD/YfcXm82i8ROO68QJS6VumaqQYOWwy3pk2+kV5pKTZD28VRbDLklqJUmRhTc7crKOMmq0V6PzzFbhBu2kiOjylaEMgnlAUSgEn6I+g6NHWlwBOa9V+TjBuBz4G1F+hGMgSAXaH/ZgmZpp+DCLIiIiNH7CcdfPlW0gkFeClWHIkpks64Ek2ZLX5fUTPrhBlpzs4jcLq6b9aqMFm9tr07EErT2coIFDGmn4bVblnPmpVRrBHnxK+gyOHmlxtSYHW1/qQBFofyOCSUCG44MHD+r777/XokWLtH37dh0+fFjR0dHq3LmzRo8erQ4dOvi7iAAKCKapme6+M1InTpwIjMFoflCuYHXymGwH15uLayTJmrxO1qzDxR7HsFjlqNMyrzU4tr0cDTvIUeccRVvDNH5AvqnTbvP/RVOwCfbgU9JncNXq4O5LjeAWkOF42rRp+uijj9S0aVP16NFDderU0a5du7RgwQItWLBAb775pq644gp/FxNAPsE2NVMwj/I/UyUGK3uOrAe3ynpg3ekll1O3l7hfR42GcsS2l905p3D9NlKV6oVeF+yDyHDmSrqLtGbt6QvWzz6v6nanB6hoARmO27dvr08//VRdu3Z1e3zlypUaPny4nn/+eV188cWqUsW7gzMAnJmAmh6sBAQ0k2HIkr7HnDnC7Ct8aJMs9lPFb1a1hrnKXPu8INygnYyo+iUeLhQGkaHieLqgzn+nR+JzgooXkOH4kksu8fh4165d1a1bNy1evFh//fWXEhISfFwyACUJhhbZgqPfK1VAy041W4OTXGHYciK92E0Ma7gc9eLNrhF5XSSMmOaSpWzdIUJhEBkqVrD3pUZoCMhwXJywsDC3/wMILIHeIpsX0I5XjoCWc0LWlE2yHVjnmk/Ymr6nxM0ctZrKHtshb3GN2PZy1G8thVU94+IUFXzsdkNdOnsOPoE0mBMVL9j7UiM0BFXC3L9/v/744w/Vq1dPcXFx/i4OgAKC4Za53W7ovnuqacjgk26PB33LlOGQJXW7bAfyT6O2RRZHbvGbVYvJ6yMc297sL9xOqhZTIUUsKvjYbBatWm2oU8fCwTjQBnMCCH0WwzA8rE4feHJycjRixAitWLFCr732mq699toiX+twOGS10soA+NJ7H2Rr/ITjuu+earr7zsgSH8eZMTKSZexdLWPvmrz/718nncwsfqOwCFkatZflrE6u/1SrqSwW/4fPgp8TPjcA/CUoWo4dDof+9a9/acWKFRo8eHCxwViS0tOL7z9XEWJiYpRWhmVLERyo19LLynJo9EiLhgw+qbS0062yQwZLJ05YlJV13O1xfwq6ej2VJdvBDa7ZI6zJibJmHix2E0MWOeqcc3rAXGyCHHVaSbZw9xcePer6pz/nqnZ+TsZPOK4PPjruGsxZ8PNUnKCrV5QK9Rqa/FWvMTEl3xkL+HBsGIaefvppffPNN7r66qv1/PPP+7tIADwI1b6CPg+MjlxZD2/N6yNs9hW2pm6TxXAUv1lUA9c0aq7uER6mUSuOv+eqDobBnJVFsCzqA1SEgA7HDodD//73vzVnzhwNHDhQr776Kt0lAPhUhQZGw5AlY7/ZRzjx9CpzuSeK36xKddkbJJweMBfbXkaNBuUvh6m4uaq7dPYcVr0ZlAJlMCfB0P8XSoA/BWw4zh+Mr7jiCr3++uuy2Wz+LhaASsari5ucSJcteb2szuWWk5NkzT5S7CaGNUyOuq3M7hEdZI9NkBHTQrJWzO9DT3NVd+ksrVpdOKx6MygF0mBOgmHwLeoDeFNAhuP8wfiyyy7TmDFjCMYA/KZci5vknsqbRs05n/CBRFmP7irxWI7oJnldIxq2z2sVrtdaCo/w1qmUSsHuDe+8ZS0UVr0ZlAJt/mOCYZ5gWtQH8KaADMfvvvuu5syZo8jISDVv3lzvvfdeoddcfPHFat26tR9KB5QOt2ZDS7H9YQ2HLGm78rpHHDC7R6RslsWRU+w+jYjofFOoJcgemyBF1q7gMylZcd0bKiIoBeLCDwTDPPQDR2UUkOF43759kqTs7Gy9//77Hl/TuHFjwjECGrdmQ0v+wFjDelgLP1qvS9okmotrrJflZEax2xu2KnLUb3N6wFzD9jKim0gBMI1afiV1b6iIoFTWwZy+uvAkGAZOP3DAlwIyHL/66qt69dVX/V0M4IxwazZE5GTrp6kbdOqPRM26IUnnVE2U9dgB6ZikZUVv5qh9juzOAXMNO8hRt5Vkq+KzYpdHSd0b1qwNjKBU1IVn/mXBvaGyB8NA6gcO+FJAhmMgVHi6NdupY9Gvp7uFnznssh75+/TMEQcSZTm8VdfJIbWVdMr8r+Bm1evKEdtBKw600+QF7dV1YDsNHV7T16U/Y8V1b1iz1tCq1QqIoFT0hedxr114Bmsw9FareqD1Ay8rurXhTBCOAxRf7NBR8NZsl850twgIhiHLsQPmfMLmksuHNsqSk138ZuGRcjRoq7VH2mv6onZSowQ9/0YjTZkmffxZXv0NDeDQUJyifqdMmeoejCX/ByVPF56elgUvj2AOht7qzhWI/cDLgm5tOBOE4wBV1i82YTpwFbw1K+WFDLpb+NiJDNkOrpc1OVG5RzYrcs8qWbMOF7uJYbGdnkbN7CvsqHOOZLUpXlKL6nn1tuiS0B6wFahBqeCF5913RnplFcZAPd/S8FZ3rmBf1IdubTgTFsMwDH8Xwtv8tRyht49b1G09T1/sop7jl8GZOdN6La4Opbxf3M7QTB15kf2UrClbZEteZw6YS5I1dXuJmzlqNjo9e0TD9nLUby2FRxa7Td8BDlc4+3V+xV6AchHszvl9cn6HvNVyHAoKvjfB/PvlTH4Ph9L7EGpYPhrlUpaphLhKDjwl3ZodPdLi+oVdWUfCe1LmAGgYshzdba4yZy65nLJJFnsJ06hVrSl7bLvTQbhBgozqdctUVl8P2OJW8WmeLjzHTziuEyf4fSf5fqaNQL1wY8YRlAfhOMCV5YvNvJyBpaRbs6tWB+dI+Ir+I1hSALxveJps25NcA+ZsyUmynEwvdp+GLVyOeq1dXSOi4nvpqDXmjKZR88eALS6C8xR14RkREaHxE467fq7MuHA7ffxg/D0L/yIcB7iyfrG5Sg4cJQXENWsDY+R/WVX0H8H8ATDMOK5hF2/Wqu8S1XJLon67NknRqXulr4rfhyOmudviGo5650php6dRs8TESF7sLlOw3Pl/9jYugou+8Lz7zkidOHEioPsE+wIXbnmCdcYR+B/hOIAV9cVes9bQO28VDl55I8q5Sg50gTYSvqwtwRX2R9BhlzV1u6zJibqzUZIGD0pU7ZQtCptp14WS1FiSw8NmkXXcBszZY9tJEdHlK0Mp+XvAVmW/CA72wWIViQu3PIH2exbBhXAcoIr6YjvnGn3wEYdbQM5/RcxVcsXwVncCfwergsrTEuyNP4KWYwdlTV6X1z0iOUm2g+tlOZXler6+JBV4O42wCDkatDVbhRPyVpmr0cjnq8z5O5xxqxhF8ffvl0C5cPP3+4DgRjgOUEV9sd95y6oHH3Fo1erTfxA9BWOJq2Rv81Z3An8HK8/HLHtLcJn+CJ7MNKdRS8obOHcgUdasQ8WWy5BFf2e01Mb0BCWmJqhVn/YaODxOslbuX1vcKkZx/P37JVAu3Pz9PiC4Ve6/MgGsuC/2O29ZXX8Q86+61qUzV8kVKRD71HlLeVqCi/wjaM+R9fCW00E4OVHWI9tlUfGzRjqiGrhmjpi3LkFjZrTR0NuiNHyYRXumGnp1kqHDYRYNH+bVUw8q3CpGIOPCDaGCcBykCrbajXubq2RfCKQ+dd5WlpZg1x/BEdKIa/Zp8axEpSxbp2NH1yvW2CiLvfi5Zo0qUaenUTP7ChtR9U/v+38EQE/Keqs4UKfXQujhwg2hhHAcpALl1lVlFCh96rytVJ+p42n65dMk2ZYn6qvrk9QsO0mWSWm6VJLOkZRbeL+GNUyOevF5fYTNMGzUPluyeA5l9BUsWllvFQfq9FoIPXxvEUoIx0GIW1f+FYoXJp4+U1OnnFBszmZd1ckcMHcgUdb03bpaks6VlGP+V8BRaxNVb9VejoZ5YdhRr7UUHlHqstBX0HtCuSsQAgvfW4QSwnGQ4daVf4XihcmUqYYmTrLr8WE7dX2X9bL+nKi7bYm6e+BfsqXnSguL3taIqCV7bILsDTuYLcMJCqsWIxbwDRwV2RWIbhsAQhHhOMhw68p/QunCxJKV4lpd7uqj63T7NetV9Wim9GPR2xi2KnLUb5O31HJse9lj28uIPsvn06gFI3+HyIrqCkS3DQChiHAcZLh15T9Be2FyKkvWgxtkc80ekSTrsQOup5t62MSQRY46Z7sNmHPUjZNs4b4rdwjxd4isqK5AdNvI4++LHwDeRTgGSikoLkwcubIe3uo+n3DqNlkMD0vL5d+sej3XNGqO2ATZG7STqtbwUaFDnz9DZEV3BQrlGVxKy98XPwC8i3AMBCvDkCVjv6s12JacKOvBDbLknih+s/DIvNbgBu3MMNxBRo0GPip05eWPEOmrrkChOoNLadGCDoQWwjHccHswgJ1Ily15vazJiae7R2QfKXYTw2KTo26cHA3zdY+ofbZktfmo0MjP1yHSV12BQnEGl7KiBR0IHYRjuOH2YIDIPSXr4b/ypk9zhuG0nSVu5qjZ2G3AnKN+aym8WsWXF6Xi6xDpi65AoTiDS3lV9hZ0IFQQjuGG24N+YDhkObpLtgNJZhBOkjVlkyx2D5MI59+sarTZGpzg6itsRNbxUaFRVqEYIkNpBhdvoAUdCA2EYxTC7cGKZck6fLqPcHKSbMlJspzMKHYbwxYuR73Wea3BZhg2ajVjGrViFNdF6L0PspWV5fBZF6FQDZFBO4NLBQjFix+gsiIc+1mg9vEteHvQbjc0ZarnX/L0RS5GTrasBzfmtQY7u0dk7C9xM0dMi7xW4YbtZY/tIEe9OMlWpVSHDNTPlK8V30XouE+7CIVqiAyKGVx8oCIvfvg+A75HOPazQO3jW/D2YGKStGp14JUzoDjssh7Z5j5g7vBWWQx78ZtF1ikwjVqCFFGz3MUI1M+UrxXXRei+e6ppyGDfreNHiAxtFXnxw/cZ8D3CsZ8FYh/fom4PdukcOOUsa2uK11tfDEOWzGRZDyTJlrwur2X44AZZcrKL3yysmhwN2sge20H2hnmzRxg1Gnq1e0Qgfqb8paguQnffGam0NBa5hndU5MUP32fA9wjHASCQ+viWdHvQGZD9Xc6ytqaccevLyWOyHVzvWnLZmpwoa1ZKsZsYFqscdVrltQabXSQcdVpK1or/2gXSZ8rfgnEGAW6lIz++z4BvEY4DRKD8AS/N7cHEJPm9nGVtTSnT6+2nzFXmEpWbulmRu1bJkrpdFhnFlslRo6FruWV7w/Zy1G8jVanurVMus0D5TPmbpxkEHn7Q36UqHrfSURDfZ8B3CMcBIlCmACrp9uCUqVJOjuH3cjrLI5W+NcXj60dII67eI9vmJFkPmN0jDm2UxX5KkmRI8vSOGFVryN6gnVtfYaN6vYo4zXILlM+UPxXVRSgiIltDBvu7dEXjVnpg8meLPt9nwHcIxwEgWKYACsRylrU1ZfiNR7X1+0S1rpmohJgk9chKkmXS0WK3MazhctSLz5tGrWGC7LHtZcQ0lyyBe1s7EOvK14rrIjR+wnGdOBHYIZNb6YHHWy36ZQ3ZfJ8B3yIc+1mwzH8aqOUstjUl54SsKZvyZo44YM4rnL5H75yXbwcnCu/TUauZaz7hyLheSo9oJIVV9cn5eEOg1pWvFddFKCIiQllZxxXos0SU9uKPPsq+4a0W/bKEbL7PgO8Rjv0sWOY/DcRyuv3RuNXQ15O36a/5idqRmaQ2NZNkPbxFFkdusftIPRmjjKj2atg1wdVfWNVquZ63xsRIaWkVfCbeFWh15a/gVtw+g2W2itLeSqePsu94o0W/LCE70L7PQGVgMQyj+FFGQSjND2EmJibGL8f1N38Fn1mTDyrxx0Td3CdJHesmyXYwSZZTWcVuc8JeValV26puh/ZyNGgne8MOmvxVI308ueg/bpW1Xr2pqD/63upDW57PYDDUa1G30ot6v8r6+lDky3rtO8DhunD5dX75fsc568h58VOZ6qosguH7irLzV73GxMSU+BpajnFGfNJidSpLtuT15uIaedOojcg8KJ0v6bikPYU3MWSRo845rgFzc5a109EqrTTstio6le91w2+TZDFofalAFT24LBRbTctzK50+yr7jrcFxzEABBCbCMc6I14OPI9c1jZrtQGLefMJHtpU8jVpUA1e3iLz/t3ObRu3q9iWdA3+UKlJFBrdQnNmhvLfSCVsVz5uD45iBAghMhGOcsXIHH8OQJWOfa6ll24HEvGnUcj2Mksu/WZXqsjdIyFtco2F7ORokyKjRwFungwpSkcEt1FpNy7viGmGrYnlzcBwzUACBi3AMryhV8Dl+NG+VOVercJKsx1OL3a9hDZOjbpwZhDvIHpsgo/bZAT2NGjyr6OBW2VtNCVsVz1uD45iBAghshGN4RcHgM+2TE7rtkr9cIdiWnCjr0V0l7scR3cS11LI9tr0c9VpL4RE+OIPTmBbL+3wR3CpzqylhyzfK26JfEDNQAIGNcIwzNuUTu+Z/vlNjhiapzzlJStuQpNopmxQ+o/hp1IyIaHM+4dNLLqtayaNIK1r+AV75lxkO5gFe/uSL4FbZW00JW8HFWyEbQMUgHKPMLFmHzZkjEpW8OlG3Za/Xff2PSZmS1kkNpEJrLhu2KnLUb306DDdsLyO6iWQJvD8C+YObc5nhYB/g5U8VHdxoNSVsAYA3EY5RvJxsWQ9ukM05YC45UdZjB1xPN5Wk8MKbOWqfo7+yEpRsbadugzrIUS9OslXxWbHPlDNMjZ9wXB98xBykZ6KigxutpgAAb2IREC8JiUnKHbmyHtnmPmDuyFZZDEfxm1WvK0dsB3PmiHZ5q8xVreGjQlcsb0z0j8ATEt9XFEK9hibqNTSxCAgCj2HIcuyAawo1W7I5jVpOdvGbhUfK0aBtXh/h2A5yNEyQERV7xt0jAnEQXGUe4AUAQGVFOPayQAx5kqQTGaenUTNXmbNmHS52E8NilaNOq9MzR8S2l6POOZLV5vXieWuVM2+9/87j3ndPNQ0ZfLLSDfACAKCyIhx7WUAsZWs/JWvKFtmS15nTqCXJmrq9xM0cNRu5zR7haNBGCo+s+PLKe6ucleX9LypIO1/bqaN0952RSks76ZMBXgF7YQUAQCVCOPYyny9laxiyHN1ltgab8wkf2iSL/VTxm1WtaS61nGAG4gQZ1et6t2xl5I1Vzsry/hcVpFetznusS2ffDvAKiAsrIARx4QmgLAjHFaBCl7LNTpUt34A5W3KSLCfTi93EsIbLUe/cvAFz5nzCRq1mAbnKnDdWOSvt+19UkF6ztuj6qshpsXx+YQVUElx4AigLwnEF8cpStjnHZT20Ka812NlXOH1viZs5YprL3iD/KnPnSmHBMY2atwbBlfb9r9ALmXIItPIAoYALTwBlQTiuIGUOeQ67rKnbT3eNSE6UNWWLLIa92OM4qtV2GzBnb9BWqlbLuyfjI95c5aws779XLmS8KNDKA4QCLjwBlBbhuAKUJuRZjiXnmzkiSbaD62U5lVXsfo2wCHMatXzdI2o0CshV5srKm6uclTVkB9qUbYFWHpQefVsDGxeeAEqDcOxlHkPeTVlqfCpJuxcl6mBGklqEJ8madajY/RiyyFGnZb5W4QQ56raSrKFZZd5a5aysIdubrdXeEGjlQdnQtzWwceEJoDRCM2n5kZF7Sk8N+1vXdEiS7Ueze8SR7RokQ2oj6ZT5XwGOGg3zWoMbtJOjYYe87hFVqvu6+H7jrSWGyxKySxOkH36wLGdxZrzZeg7/oG9r4OLCE0BpEY69wJK6Q/Y//6tqu1bovmMbZbGflH4u+vVGlSjZY9vlLblsTqdmRNX3XYFDWFlCdumCtO94q/Uc/kXf1sDDhSeAsrAYhuHbBOADPl2r23Co+oQeRU6nZljD5KgX77a4hlG7RUBOo4bC/LX2OyqWL+q17wCH6xb+r/P5vvtCUfVKX/Dgxu/h0OSveo2JiSnxNbQcnynDIaN6XVc4dkQ3PT2fcGyCHPXbSGFV/VxIAL5E39bA4q1uWwAqB8LxmbKGKfsfMxSdk6J0W4xUreQrEgChi76tABDcCMfeULWGrLFNJW77AJUafVsBIPgRjgHASxhUCQDBj3AMAF5C31YACH4Mz62kJk52aMpUzxOVTJlqaOJkh49LBAAA4H+E40rKuZJXwYDs7DNps9HCBQAAKh+6VVRSrOQFAABQGOG4EmMlLwAAAHd0q6jkhg+zuBYqCA9nmikAAFC5EY4rOU8reQEAAFRWhONKLH8f41/nWzV6pOdBegAAAJUFfY4rKVbyAgAAKIxwXEmxkhcAAEBhhONKipW8AAAACqPPMSpEZVqBrzKdKwAAoY5wjApRmVbgq0znCgBAqKNbBSpEZVqBL1TPdeJkh2w2z+WfMtWQ3W4U2z0HAIBgRDhGhalMK/CF4rk6W8Ql95lL8gd/AABCDc0+qFCVaQW+UDvX4cMshea+DoUWcQAAikM4RoWqTCvwheK55g/IfQc4CMYAgJBHOEaFqUwr8IXyuYZaizgAAMWhzzEqRGVagS/Uz9VTi3gwnw8AAMUhHKNCVKYV+EL5XAsGf+fPUnAHfgAAikI4RoWoTCvwheq5hnqLOAAAnhCOEdCYa9d/QrlFHACAohCOEdCYa9d/QrVFHACA4hCOEdBCdfU5AAAQmAjHCHihuPocAAAITHTWRFBgrl0AAOALhGMEhVBcfQ4AAAQewjECXiivPgcAAAILfY4R0JhrFwAA+BLhGAGNuXYBAIAvEY4R0JhrFwAA+BJ9jkPcxMmOIvvmTplqaOJkh49LBAAAELgIxyHOucJcwYDs7Mtrs9HyCgAA4ES3ihDHCnMAAAClRziuBFhhDgAAoHToVlFJsMIcAABAyQjHlQQrzAEAAJSMcFwJsMIcAABA6dDnOMSxwhwAAEDpEY5DXKCtMDdxskM2m+fBgFOmGrLbjWIX/kD58d4DAFAywnGIC7QV5pzzLp8+fp78LdyoGLz3AACUjHAMn2LeZf/hvQcAoGSEY/gc8y77D+89AADFo4Mh/IJ5l/2H9x4AgKIRjuEXzLvsP7z3AAAUjXAMn2PeZf/hvQcAoHj0OYZPMe+y//DeAwBQMsIxfCrQ5l2uTHjvAQAomcUwjJC7n5qWlubzY8bExPjluKhY1Gtool5DE/UamqjX0OSveo2JiSnxNfQ5BgAAAEyEYwAAAMBEOC6niZMdRY7wnzLV0MTJDh+XCAAAAGeKcFxONpvnKbCcMwLYbAxsAgAACDYBPVtFYmKixo0bp7Vr1yonJ0ctW7bUbbfdpquuusrfRSs0BdbDD3qeKgsAAADBI2DD8bJlyzRq1CiFh4fryiuvVI0aNfTTTz/pscce0759+3TXXXf5u4huAfmTaUeUkyOCMQAAQBALyKnccnNzdfnllys5OVkzZ85UmzZtJEmZmZkaMmSIduzYoblz56p58+Yet/f11CB9Bzhcy/H+Op+eKqGEKYRCE/UamqjX0ES9hiamciujpUuXavfu3Ro4cKArGEtSVFSU7rnnHuXm5mrOnDl+LOFpU6YarmCckyOW4QUAAAhiARmOly9fLknq1atXoed69uzp9hp/yt/HeO3KOho90vMgPQAAAASHgOxzvHPnTklSs2bNCj0XHR2tmJgY7dq1y8elcudp8F3BQXr0PQYAAAguARmOMzMzJUk1atTw+HxUVJSSk5OL3D46OlpWa8U2ilepkq377pHuvjPS9VhMTIweflCKiMiWwyHFxEQWswcEi9L0T0LwoV5DE/UamqjX0BSo9RqQ4fhMpaenV/gxhg7J+39a2klJ7h3Lhwx2fw7Bi4EgoYl6DU3Ua2iiXkMTA/LKKCoqSpJ07Ngxj89nZmYW2aoMAAAAlFdAhmPnFG2e+hWnp6crLS3NY39kAAAA4EwEZDg+77zzJEmLFy8u9NySJUskSeeff75PywQAAIDQF5Dh+IILLlCTJk303XffadOmTa7HMzMzNWHCBIWFhWnQoEF+LCEAAABCUUAOyAsLC9OLL76o0aNHa+jQoRo4cKCioqL0008/ae/evXrooYfUokULfxcTAAAAISYgw7Ekde/eXdOnT9fYsWP1/fffKycnRy1bttSDDz6oq6++2t/FAwAAQAgK2HAsSe3bt9fHH3/s72IAAACgkgjIPscAAACAPxCOAQAAABPhGAAAADARjgEAAAAT4RgAAAAwEY4BAAAAE+EYAAAAMBGOAQAAABPhGAAAADARjgEAAAAT4RgAAAAwEY4BAAAAE+EYAAAAMBGOAQAAABPhGAAAADBZDMMw/F0IAAAAIBDQcgwAAACYCMcAAACAiXAMAAAAmAjHAAAAgIlwDAAAAJjC/F2AQJWYmKhx48Zp7dq1ysnJUcuWLXXbbbfpqquuKvU+HA6Hpk+frpkzZ2rXrl2KjIxUt27d9PDDD6t58+YVV3gU6UzrdeXKlVqwYIGWL1+uffv2KTs7W40bN1b//v115513qmbNmhV8BvDEG9/X/HJycnTDDTdo8+bNatGihX744Qcvlxil4a16zczM1KRJk/TTTz9pz549Cg8PV5MmTdS/f3/dd999FVR6FMUb9ZqRkaHJkydrwYIF2rt3r6pUqaKzzjpLgwYN0o033qiqVatW4BmgoK+//lqrVq3S+vXrtWXLFuXk5OiVV17RddddV6b9BEpuYio3D5YtW6ZRo0YpPDxcV155pWrUqKGffvpJe/fu1cMPP6y77rqrVPt55pln9Pnnn6tly5bq06ePjhw5onnz5qlq1ar67LPP1LJlywo+E+TnjXrt2bOn0tLS1KVLF7Vu3VoWi0XLly/Xxo0b1bRpU3322WeqU6eOD84GTt76vub3zjvvaMqUKcrOziYc+4m36nX//v267bbbtGfPHvXo0UOtW7fWqVOntHv3bu3fv1/ffvttBZ8J8vNGvWZkZOi6667Tnj171KVLF3Xo0EGnTp3SokWLtHv3bnXv3l2TJ0+W1crNcV/p16+f9u3bp5iYGEVGRmrfvn3lCscBk5sMuMnJyTEuvvhio127dsaGDRtcjx87dsy48sorjTZt2hg7duwocT9//vmnERcXZwwdOtQ4efKk6/E//vjDiI+PN26++eaKKD6K4K16/eCDD4yDBw+6PeZwOIznnnvOiIuLM/7zn/94u+gohrfqNb/169cbbdq0MaZOnWrExcUZl156qZdLjZJ4q15zc3ON66+/3mjfvr3x559/ejwOfMdb9frhhx8acXFxxssvv+z2+MmTJ43rr7/eiIuLM5YvX+7t4qMYS5YsMfbu3WsYRt7fybi4OGP27Nll2kcg5SYuqwpYunSpdu/erYEDB6pNmzaux6OionTPPfcoNzdXc+bMKXE/s2bNkiQ99NBDqlKliuvxCy64QL169dKKFSu0Y8cO758APPJWvd5xxx2qX7++22MWi0X33HOPJGnFihXeLTiK5a16dTp16pSefPJJdejQQbfccktFFBml4K16/fHHH5WUlKSRI0eqe/fuhZ4PC6NnoS95q1737NkjSerTp4/b41WqVFHPnj0lSUeOHPFiyVGSHj16qHHjxme0j0DKTYTjApYvXy5J6tWrV6HnnF8652uKs2zZMkVGRqpz586FnnPumyDlO96q16I4/8jabLZy7wNl5+16HT9+vHbt2qWXXnpJFovFO4VEmXmrXufNmydJuuyyy3TgwAHNmDFDH374ob7//ntlZWV5scQoDW/Va6tWrSRJv//+u9vjOTk5+uOPPxQREaFOnTqdaXHhY4GUm7hsLmDnzp2SpGbNmhV6Ljo6WjExMdq1a1ex+8jOzlZKSori4uI8hiVnp3LnsVDxvFGvxZk9e7ak07/g4RverNfExER9/PHHevjhh9WiRQtvFhNl5K16Xb9+vSRp1apVeuWVV3Tq1CnXc7Vr19bbb7+tbt26eafQKJG36vXGG2/U119/rUmTJmn9+vVq166dcnJy9Pvvvys9PV1vvvmmGjRo4O3iowIFWm6i5biAzMxMSVKNGjU8Ph8VFaVjx44Vuw/n81FRUUXuI/+xUPG8Ua9F2bRpk959913VqVNHo0ePLncZUXbeqtdTp07pqaeeUuvWrTVy5EivlhFl5616dd5af/HFF3Xbbbfpt99+059//qmnn35ax44d07333qtDhw55r+AolrfqNSIiQtOmTdPVV1+t5cuXa9KkSZo2bZqry4anlkcEtkDLTYRj4Azs2bNHd955p+x2u9566y3Vrl3b30VCObz99tvatWuXXn75ZbrGhBDDnIzpoosu0mOPPabY2FjVrl1bt956q4YPH65jx47piy++8HMpUVapqakaMWKE1q1bpw8//FArV67UkiVL9Pzzz2vOnDkaPHiw0tPT/V1MBDHCcQHOq5Oirl4zMzOLvOp1cj5f1BWO8/GirpDgfd6o14L27dun2267TampqRo7dqzHAT+oWN6o1w0bNmjKlCm66667FB8f7/Uyouy89X117qdfv36Fnuvbt6+k010vUPG8Va+vvvqq1qxZo7Fjx6pPnz6qUaOG6tatq8GDB+vxxx/Xnj179Mknn3i17KhYgZabCMcFOPu1eOr3lJ6errS0NI/9pfKLjIxUvXr1tHfvXtnt9kLPO/vMsBCI73ijXvPbu3evbr31Vh06dEhvv/226w8tfMsb9frXX3/Jbrdr3Lhxio+Pd/tPknbs2KH4+Hh17drV6+WHZ976vjr7jntanMf52MmTJ8+gpCgLb9Xrb7/9plq1auncc88t9JyzkWLDhg1nVlj4VKDlJsJxAeedd54kafHixYWeW7JkiSTp/PPPL3E/559/vrKzs7V69epCzzn37TwWKp636lXKC8bDhg3ToUOH9N///lcXX3yx9wqKMvFGvTZv3lw33HCDx/+kvBaNG264Qddee613C48ieev76gxKf//9d6HnnI+d6fRTKD1v1eupU6eUmZnpNsDSKTU1VZLcpgJDcAio3OSzGZWDRE5OjtG/f3+jXbt2xsaNG12P55+kfPv27a7Hjxw5Yvz999/GkSNH3PYTSJNZw3v1umfPHqNv375GmzZtjB9//NFn5Ydn3qrXorAIiH94q153795ttGvXzrjggguM5ORkt/1cc801RlxcnPHHH39U/AnBMAzv1evIkSONuLg447///a/b4ydPnnQ9N23atAo9FxStpEVAgiE3sXy0B0uXLtXo0aMVHh6ugQMHKioqyrW85UMPPaS7777b9dpx48Zp/Pjxuu+++3T//fe77efpp5/WrFmz/L8MIiR5p16dS2R27NjR41ydkgp9DlCxvPV99SQ+Pp7lo/3EW/U6bdo0vfjii6pVq5YGDBigKlWqaOHChdq3b59uuukmvfDCC74+tUrNG/W6adMm3XzzzcrKylL79u3VuXNnnTx5UosXL9aePXvUtm1bzZgxQ1WrVvXHKVZKs2bN0qpVqyRJW7Zs0YYNG9S5c2dXN5mLL77YdZc1GHIT8xx70L17d02fPl1jx47V999/r5ycHLVs2VIPPvigrr766lLv54UXXlB8fLxmzpypadOmKTIyUn379mUeVT/xRr3u27dPkrR27VqtXbvW42sIx77lre8rAou36vXWW29V48aNNXHiRM2dO1d2u10tW7bUXXfdpcGDB1fgGcATb9Rr69atNWfOHH3wwQdaunSpPv30U9lsNjVt2lT333+/Ro0aRTD2sVWrVunLL790e2z16tWuLhKNGzcuVRfEQMlNtBwDAAAAJgbkAQAAACbCMQAAAGAiHAMAAAAmwjEAAABgIhwDAAAAJsIxAAAAYCIcAwAAACbCMQAAAGAiHAMAAAAmwjEAAABgIhwDAAAAJsIxAAAAYCIcAwAAACbCMQCEkIceekjx8fEaM2ZMoee2bdumDh06qHPnztqzZ48fSgcAgY9wDAAh5Pnnn1dsbKwmTZqkZcuWuR7PycnRY489phMnTujpp59WkyZN/FhKAAhchGMACCHR0dF67bXXJElPPPGEMjIyJElvv/22Nm7cqEsvvVTXXXedP4sIAAHNYhiG4e9CAAC86/XXX9fEiRM1cOBADR48WMOHD1fdunX17bffqlatWv4uHgAELMIxAISgU6dO6aabbtLGjRsVFRWlrKwsTZo0ST169PB30QAgoNGtAgBCUJUqVfTKK69IkjIzM3XLLbcQjAGgFAjHABCivv/+e9e/N27cKIfD4cfSAEBwIBwDQAhauXKlPvzwQ9WvX1/du3fXqlWr9OGHH/q7WAAQ8OhzDAAhJjMzU1dffbX279+vjz/+WHFxcbrqqquUlZWlGTNmKCEhwd9FBICARcsxAISY//znP9q3b59uueUW9erVS/Xr19eLL77omuv4+PHj/i4iAAQswjEAhJC5c+fq22+/VatWrfT444+7Hh8wYICuu+467dy50zVQDwBQGN0qACBEHDhwQFdffbWOHz+uWbNmqXXr1m7PZ2Vl6ZprrtGePXs0YcIE9e/f308lBYDARTgGAAAATHSrAAAAAEyEYwAAAMBEOAYAAABMhGMAAADARDgGAAAATIRjAAAAwEQ4BgAAAEyEYwAAAMBEOAYAAABMhGMAAADARDgGAAAATIRjAAAAwPT/hqVDw6/62RMAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 700x700 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(7, 7))\n",
    "ax = fig.add_subplot(111, xlabel=\"x\", ylabel=\"y\", title=\"Generated data and underlying model\")\n",
    "ax.plot(x_out, y_out, \"x\", label=\"sampled data\")\n",
    "ax.plot(x, true_regression_line, label=\"true regression line\", lw=2.0)\n",
    "plt.legend(loc=0);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "295964ad",
   "metadata": {},
   "source": [
    "To highlight the problem, first fit a standard normally-distributed linear regression."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "cdb8834d",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [sigma, Intercept, x]\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "5a850491b4614dc48bf665c0d114b897",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 1 seconds.\n"
     ]
    }
   ],
   "source": [
    "# Note, \"gaussian\" is the default argument for family. Added to be explicit.\n",
    "gauss_model = bmb.Model(\"y ~ x\", data, family=\"gaussian\")\n",
    "gauss_fitted = gauss_model.fit(idata_kwargs={\"log_likelihood\": True})\n",
    "gauss_model.predict(gauss_fitted, kind=\"response\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "2869adc9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>hdi_3%</th>\n",
       "      <th>hdi_97%</th>\n",
       "      <th>mcse_mean</th>\n",
       "      <th>mcse_sd</th>\n",
       "      <th>ess_bulk</th>\n",
       "      <th>ess_tail</th>\n",
       "      <th>r_hat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>sigma</th>\n",
       "      <td>1.220</td>\n",
       "      <td>0.088</td>\n",
       "      <td>1.059</td>\n",
       "      <td>1.385</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.001</td>\n",
       "      <td>5472.0</td>\n",
       "      <td>2741.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Intercept</th>\n",
       "      <td>1.509</td>\n",
       "      <td>0.237</td>\n",
       "      <td>1.066</td>\n",
       "      <td>1.947</td>\n",
       "      <td>0.003</td>\n",
       "      <td>0.004</td>\n",
       "      <td>6174.0</td>\n",
       "      <td>3141.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>x</th>\n",
       "      <td>1.153</td>\n",
       "      <td>0.414</td>\n",
       "      <td>0.424</td>\n",
       "      <td>1.946</td>\n",
       "      <td>0.005</td>\n",
       "      <td>0.007</td>\n",
       "      <td>6076.0</td>\n",
       "      <td>3355.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            mean     sd  hdi_3%  hdi_97%  mcse_mean  mcse_sd  ess_bulk  \\\n",
       "sigma      1.220  0.088   1.059    1.385      0.001    0.001    5472.0   \n",
       "Intercept  1.509  0.237   1.066    1.947      0.003    0.004    6174.0   \n",
       "x          1.153  0.414   0.424    1.946      0.005    0.007    6076.0   \n",
       "\n",
       "           ess_tail  r_hat  \n",
       "sigma        2741.0    1.0  \n",
       "Intercept    3141.0    1.0  \n",
       "x            3355.0    1.0  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.summary(gauss_fitted, var_names=\"~mu\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c0c2b7d0",
   "metadata": {},
   "source": [
    "Remember, the true intercept was 1, the true slope was 2. The recovered intercept is much higher, and the slope is much lower, so the influence of the outliers is apparent.\n",
    "\n",
    "Visually, looking at the recovered regression line and posterior predictive HDI highlights the problem further."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "336fb8b6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAscAAAH/CAYAAAC7N3BzAAAAOnRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjEwLjYsIGh0dHBzOi8vbWF0cGxvdGxpYi5vcmcvq6yFwwAAAAlwSFlzAAAPYQAAD2EBqD+naQAAotFJREFUeJzs3Xd4VGX6PvD7nDO9JJkUCCWAUgVUsCxgL6gYEMW+6iKCZdV1dXfd7vZddXd/fte1rgKKuHYBRUAFdRVFQWkKqIhIryE9k0w95/fHKTlTUiZtJpn7c125SDKTmTOZMLnznud9HkFRFAVERERERAQx3QdARERERJQpGI6JiIiIiDQMx0REREREGoZjIiIiIiINwzERERERkYbhmIiIiIhIw3BMRERERKRhOCYiIiIi0li68s4qKyu78u5i5Obmorq6Om33T12Hz3V24POcPfhcZwc+z9kjnc+1z+dr8TpZs3IsilnzULMen+vswOc5e/C5zg58nrNHpj/XmX10RERERERdiOGYiIiIiEjDcExEREREpGE4JiIiIiLSMBwTEREREWkYjomIiIiINAzHREREREQahmMiIiIiIg3DMRERERGRhuGYiIiIiEjDcExEREREpGE4JiIiIiLSMBwTEREREWkYjomIiIiINAzHREREREQahmMiIiIiIg3DMXV7c5+WMW++kvSyefMVzH1a7uIjIqJMsH//fowfPx5//vOf030oRNSNMBxTtydJAuY8pSQE5HnzFcx5SoEkCWk6MiLq7saPH49bb7013YdBRF3Iku4DIGqvGdPV8DvnKTUc/+TOxmB840zBuJyIiIioJQzH1COYA/Izz5YjHAaDMREREaWM4Zh6jBnTBTzzrIJwGLBawWBM1AHmPi1DkpL/oTlvvoJoVMGsG9JboReNRvHcc89h8eLFOHz4MHr16oWLLroIEydOTLjuunXr8Oabb+KLL75AWVkZAGDgwIG45JJLcMkll8Rc7/bbbwcAbNiwAePHjzcuu+eeezBlyhTU1dVh4cKF+OSTT7Bnzx5UVVUhLy8PJ598MmbNmoX+/ft37gMnok7BcEw9xrz5jcE4HFY/ZkAmah+9ph+I/YPTXLqUbvfffz/eeOMN9O3bF5dddhlCoRBeeOEFfPHFFwnXffbZZ7F3716MGjUKZ555Jurq6vDJJ5/g/vvvx65du3DnnXcCAPr06YNZs2Zh7ty5KC4uxuTJk43bGDZsGABg586dmD17Nk488USceeaZcDgc2LVrF5YvX45Vq1bhmWeeQZ8+fbrmm0BEHYbhmHoE8y/qn9yZj3/9uyLpL3QiSk18Tf+M6UJG1fSvW7cOb7zxBoYOHYonn3wSTqcTAHD99ddj+vTpCdf/xS9+gb59+8Z8LhKJ4Kc//SlefvllXHXVVSguLkbfvn1x0003Ye7cuejTpw9uuummhNsaNGgQlixZgtzc3IRjuuOOO/D000/jN7/5TQc+WiLqCuxWQd1esl/UM6YLuHFm8i4WRJQa8/+ns8+TMyYYA8Cbb74JAJg5c6YRjAGgV69euPLKKxOuHx+MAcBisWDatGmIRqNYt25dq+/b4/EkBGMAOPHEE3HUUUfhs88+a/VtEVHm4MoxdXvRaPJf1PrH0agCIP2/xIm6s0yt6d+2bRsAYMyYMQmXJfuc3+/H888/jw8++AD79u1DQ0NDzOVHjhxJ6f7XrVuHl156CVu2bEFVVRWi0ahxmdVqTem2iCgzMBxTt9fcZiD1F3hm/BIn6s4ytabf7/dDFEXk5eUlXJafnx/zcTgcxm233YatW7di2LBhmDRpEnJzcyFJEg4cOIBly5YhFAq1+r7fffdd3HPPPXA6nRg/fjz69OkDh8MBAFi6dCkOHjzYrsdGROnBcExERM2KL13SPwbSv4LsdrshyzKqqqrg8/liLquoqIj5eOXKldi6dSumTp2aUAu8YsUKLFu2LKX7njNnDmw2G+bNm4cBAwbEXPbOO++kdFtElDlYc0xERE3K9Jr+oUOHAgA2btyYcFn85/bt2wcAOP3001u8rk4URchy8hH0+/btw6BBgxKCcVlZGfbu3dvCkRNRpmI4JiKiJjVX03/jTEGr6U+fCy+8EADw1FNPxdQPHz58GC+//HLMdYuLiwEAn3/+eczn169fj9dffz3p7efk5ODw4cNJLysuLsbevXtRXl5ufC4YDOIf//hHTO0xEXUvLKsgIqImZXpN/4knnogpU6ZgyZIluPbaa3HmmWciHA7jnXfewahRo7Bq1Srjuqeddhr69OmD//73v/juu+9w9NFHY/fu3Vi1ahXOOOMM/O9//0t6+++++y5+/etfY9iwYZAkCaeccgqGDBmCK664Ag888ACuv/56nH322YhGo/j0008BqCva+mZBIupeGI6JiKhb+/Wvf40BAwbg9ddfx6uvvopevXrh+9//Ps4999yYcOxyufDoo4/i4YcfxsaNG7F+/XocffTR+OMf/4j8/Pyk4finP/0pALUrxQcffABZlpGfn48hQ4bg8ssvh8ViwSuvvILFixfD4/HglFNOwa233orf/va3Xfb4iahjCYqidNk5scrKyq66qwQ+ny+t909dh891duDznD34XGcHPs/ZI53PdfzG3WRYc0xEREREpGE4JiIiIiLSMBwTEREREWkYjomIiIiINAzHREREREQahmMiIiIiIg3DMRERERGRhuGYiIiIiEjDcExEREREpGE4JiIiIiLSMBwTEREREWkYjomIiIiINAzHREREREQahmMiIiJql9mzZ2P8+PFYt25dug+lR7jkkktwySWXpPswDOPHj8ett94a87me/Jxb0n0AREREbbV//35ceumlMZ+TJAn5+fk47rjjcN111+GYY45J09ERUXfEcExERN1e//79ccEFFwAAAoEAvv76a7z77rv44IMP8PDDD2Ps2LFpPkKi1nvkkUfSfQgtuuKKK3DeeeehuLg43YfS4RiOiYio2+vfvz9uuummmM/Nnz8fjz32GJ588kk8/vjjaToyotT1798/3YfQory8POTl5aX7MDoFwzEREfVIF110ER577DF8/fXXCZeFw2G88soreOutt7B7926IooihQ4fi2muvxRlnnJH0+gsXLsTbb7+NnTt3QlEU9O7dG+PHj8fMmTORk5NjXPe7777D3LlzsX79etTV1aGwsBBnnnkmbrjhBuTm5hrXu+yyy1BZWYlly5bB4XAk3Ocdd9yBtWvXYtGiRTGrcytXrsTLL7+MrVu3IhgMon///pg8eTKuvvpqSJJkXG/JkiX461//invuuQc+nw/z58/Htm3bkJOTg9dee61N34dDhw7hkUcewZo1axAOhzFixAjcfPPNrXtCNHopTGlpKaZPn47HH38cGzduRHV1NRYuXIi+ffum9DgB9WzB7NmzsWLFClRVVaF///648sorUVJSgttvvx2zZs2K+eNp/PjxGDt2LP70pz/hP//5D1avXo3Kyko88sgjOPHEEwEAGzZswH//+19s3rwZ9fX16N27NyZOnIgZM2YkPF/vvfceXnnlFezcuRN+vx95eXk4+uijMW3aNJx55pnG9datW4dnn30W3377Laqrq5Gbm4uSkhJMmjQJF198sXE9vd5Yf57Mj/PZZ5/FO++8gwMHDsDhcGD06NGYMWMGjjvuuJjrzp49G3PnzsWjjz6KyspKzJ8/H7t27YLH48E555yD22+/PenPXWuZb1//npmf21mzZuGRRx7B2rVrEQ6HMXr0aNx5550YOnRowm1VVFRg/vz5+Oijj3Do0CG4XC6MHTsWN910EwYPHtzmY2wrhmMiIurR4oNUKBTCXXfdhfXr12PYsGG46KKLEIlE8PHHH+MXv/gFfvazn+GKK64wrh8MBnHXXXdhw4YNKCkpweTJk2Gz2bBnzx4sWrQIpaWlRjj+4osvcOeddyIUCuGcc85Bnz59sHnzZrz44otYtWoV5syZYwTkSZMmYe7cuVi5ciXOP//8mGM8cuQI1q1bhzFjxsQE48cffxzPPPMMevXqhbPOOgtutxsbN27Eww8/jC1btuDee+9NePzvvfce1qxZg9NOOw2XXnop6uvr2/R9OHLkCG688UaUlZVh/PjxGD58OHbu3Ikf//jHRjhKxd69e3HjjTfiqKOOQmlpKYLBIKxWa8qPMxqN4mc/+xnWrVuHoUOH4vzzz0dNTQ0eeughnHDCCU3ef01NDW666Sbk5ORg4sSJCIfDcLvdAICFCxfin//8J7xeL0477TT4fD58+eWXmDdvHtatW4fHHnvMONYFCxbgn//8p/FHUG5uLo4cOYIvv/wSH3zwgRGOV61ahbvvvhterxenn346CgsLUVlZiW3btuHtt9+OCcfJhEIh/OhHP8LmzZsxfPhwXHXVVaisrMQ777yDNWvW4K9//SvOPvvshK9bsGABPvnkE5x++uk44YQTsHr1arzyyiuorq7Gn//859SetFY6cOAAZs2ahaOOOgpTpkzBvn37sHLlStx+++144YUX4PP5jOvu3bsXt912G8rKyjBu3DicccYZqKysxP/+9z+sWbMGDz/8MEaPHt0px9kUhmMioh7M7/c3eZkkSTErR81dVxRFOJ3ONl23vr4eiqIkXE8PIp1l0aJFAIDjjz8+5vP6qu6NN96IWbNmQRAEAOpj+tGPfoSHHnoIZ511FoqKigAATz75JDZs2IALL7wQ99xzT0zYrqurgyiqjZ9kWcZf/vIXNDQ04MEHH8T48eON6+lh75FHHsFvf/tbAI3h+K233koIx2+//TZkWcaFF15ofG7NmjV45plnMGHCBNx3333Gc6coCv7xj39g0aJFeO+993DOOefE3NYnn3yCf//73/je977Xru/DY489hrKyMtxyyy244YYbjNt57bXXcP/997f8hMT54osvMHPmTGPl2efzobKyMuXHuXTpUqxbtw6nn346/v73vxvPxzXXXIPrr7++yfvfvn07pkyZgl//+tcxz+mOHTvwwAMPYOjQoXj44YdjVvv1Up2XX34Z1157LQBg8eLFsFqtePbZZ2NCHwBUV1cb77/xxhtQFAWPPvpowuqp+XpN0VexL7jgAvzxj380nq+rrroKs2bNwn333Yfvfe97Cf+vPv30U8ybNw8DBw4EoK4+T58+HStWrMAdd9xhPL8dacOGDbjtttswffp043NPPPEEnn76aSxduhR33nmn8fk//elPKC8vx4MPPohx48YZn7/hhhswY8YM3HfffXjuuec6/Bibw1ZuREQ9WElJSZNv8cFh+PDhTV73yiuvjLnumDFjmrzulClTYq47YcKEpNfrSHv37sXs2bMxe/ZsPPzww7j11lvx5JNPwufz4Uc/+pFxPVmWsWjRIvTv3z8mEAJqWJ85cybC4TDef/99AOqq5GuvvQaPx4Of/OQnCavQHo8HLpcLgBr29uzZgwkTJsQEYwCYMWMGcnNzsXz5coTDYQDqczNq1CisWbMGlZWVMdd/++23YbfbY4Luq6++CgD41a9+FfNHjSAIuP322yEIAlasWJHwvTnjjDMSgnGq34dwOIx3330XPp8P11xzTcxtTZ06FQMGDEi435YUFBTEhOy2Ps633noLAHDzzTcbwRgABg0ahNLS0ibv32q14kc/+lHCc7po0SJEo1H89Kc/jQnGAHDdddfB5/MlfJ8tFgsslsT1xvivBwC73d6q68VbunQpLBaL8T3QDR06FJMnT0ZNTQ1WrlyZ8HVXXXWVEYwBwOFw4LzzzoOiKElLjjpC3759cd1118V87qKLLgIAfPnll8bntm7dik2bNqG0tDQmGAPAgAEDcPHFF2P79u3Yvn17pxxnU7hyTERE3d7evXsxd+7cmM/5fD488cQTMcFt165dqKmpQWFhIebMmZNwO1VVVcb19H/9fj9OPvnkmLriZLZu3QoASU/lO51OHHPMMVi9ejV2795t1FFeeOGF2LJlC1asWGH8AfLdd9/hm2++wbnnnguPx2PcxubNm+F0OrF48eKk92+3243jNhs1alTC59ryfQgGgzjxxBMTwp0oijj22GOxe/fupMfVlKFDhxqlCWapPs5vv/0WTqczaS3rsccea5xBiNe3b9+kG8o2b94MAFi9ejU+++yzhMstFkvM/Z977rl47LHHcM011+C8887DCSecgOOPPx5erzfm684991y8//77uPHGG3HeeefhxBNPxJgxY5Cfn5/0+Mz8fj/27duHQYMGoVevXgmXn3DCCVi0aBG2bdsWc7YBUP/ojaffRl1dXYv33RZDhw6N+UOlqfvUv9cVFRWYPXt2wu2Yf/66svaY4ZiIqAfbs2dPk5fFr5jp4S6Z+F90GzdubPV1P/nkk6RlFR1p/PjxePDBBwHA2OT26KOP4he/+AWeeuopY3W3pqYGgBpAv/vuuyZvr6GhAQBQW1sLAK069ayXmjQVdvTPm8PBeeedhwcffBBvv/22EY7ffPNNAGrZhVlNTQ2i0WjCHwHJjjvZ/cbfFtD674N+zPFlA83dR0ua+ppUH6ff708aGFs6rubuHwDmzZvX5Nea/eAHP0Bubi4WLVqEF154Ac8//zwkScIpp5yCn/zkJ8YGw/POOw8WiwUvvfQSXnvtNSxYsACCIOCEE07AnXfeiWHDhjV5H2352dIlK1/S/+9Ho9FWPcZUJbtPfWXdfJ/693rVqlVYtWpVk7eX7Oe6MzEcExH1YKnU9XbWdfVg2lV8Ph+uvfZa1NXV4emnn8YTTzyBn/zkJwAaj/vss8/Gfffd1+Jt6at/ZWVlLV5Xv+2Kioqkl+ufN3/vcnNzMWHCBHz44YfYs2cP+vfvj+XLlyMvLw8TJkxIuH1BEPD222+3eCytPdbWfh/0Fez48g9dU4+5rceWyuN0u93GSndHHJf+vXn33Xdb9XMuCAIuvvhiXHzxxaiursbGjRuxfPlyvPvuu9izZw+ee+45I4yeffbZOPvss+H3+/HFF1/g/fffxxtvvIE777wTL7/8csJqc/wxpfKz1R3oxxu/+TPdWHNMREQ90vXXX4+ioiIsWLAA+/fvB6DWobrdbnz11VeIRCIt3saAAQOM6+urXE3RT1+vX78+4TJ9MIndbo+p/wQaV4jfeustrF+/HocOHcLEiRMTalhHjRqF6urqlMsXkkn1+zBw4EDY7XZ89dVXCAaDMZfJsoxNmza1+5h0qT7OIUOGoKGhAdu2bUu4rC3HpZeh6Kf8U5Gbm4szzzwTf/vb33DSSSdh586d2Lt3b8L13G43JkyYgF//+teYPHkyKisrsWXLliZv1+12o1+/fti7dy8OHz6ccPmGDRsAoNnV50ykf6878uenIzAcExFRj+RwOHDdddchEong6aefBqCe2r300ktx8OBBPPTQQ0mD4fbt242VOIvFgksuuQR1dXX417/+lXAauq6uzmiNdtxxx6F///745JNP8Omnn8Zc75lnnkFVVRXOP//8hDrb0047DR6PB2+//baxuSy+pAKAUXbxt7/9LWl3g/LycuzYsaNV35tUvw9WqxXnnnsuKisr8fzzz8dcb/HixR0S2HWpPk59MuKTTz4JWZaNz+/cuRPLli1L+f4vu+wySJKE//u//8OhQ4cSLq+trY0pQVq9enXC9y8SiRh/TOk12p999lnCHxZA46pvso16ZqWlpYhEInj88cdjypS2b9+OpUuXwuPxJO1NnclGjRqFUaNGYcWKFUk3k8qynPSPzc7GsgoiIuqxLrnkEvz3v//FsmXLcP311xuT9LZu3YqXX34ZH3/8McaOHYu8vDyUlZVh+/bt2LZtG+bMmWPUcd58883YsmUL3nzzTWzevBkTJkyA1WrF/v37sXr1ajzxxBMYNmwYRFHEPffcg7vuugs//elPjT7HW7Zswdq1a9G/f3/cdtttCceod6VYvHgxDh48iJKSkqR9XSdMmICZM2fiqaeewuWXX47x48ejuLgY1dXV2Lt3Lz7//HPccsstOOqoo1r1vUn1+3Dbbbfhs88+wxNPPIHPP//c6HP88ccfY9y4cVizZk07nqm2P84pU6bgrbfewocffogZM2Zg3LhxqKmpwYoVK3DyySfjo48+SqiDb87gwYPx85//HP/85z9x5ZVX4pRTTkG/fv3g9/uxf/9+bNiwAZMnT8Yvf/lLAMA999wDh8OB448/HsXFxYhEIvj000+xY8cOTJw40ehT/dBDD+HQoUMYO3Ys+vTpA0EQ8Pnnn+PLL7/EsccemzDEI951112HVatW4c0338TOnTtx0kknoaqqCu+88w4ikQh+//vfd7uyCgD4y1/+gttuuw2/+93v8NJLL2HEiBGw2Ww4dOgQNm3ahKqqqqRdODoTwzEREfVYdrsd06dPxwMPPIC5c+fiD3/4A2w2G/71r3/hjTfewLJly/Dee+8hHA4jPz8fgwYNwrRp02J2xtvtdjz00EN45ZVX8Pbbb+P111+HJEno3bs3pk2bhj59+hjXHTNmDObMmYOnnnoKn376qTEh78orr8TMmTObHLd74YUXYvHixYhEIklXjXU333wzxowZg5dffhlr165FbW0tcnNz0bdvX8yaNctYRW2NVL8PhYWFmD17tjEhb+PGjRgxYgQeeughrF27tsPCcaqPU1/l1SfkvfTSS+jXrx9+/OMfIycnBx999FHKofGSSy7BsGHD8MILL2Djxo348MMP4fF40Lt3b1x99dUxLeJuvfVWrF69Glu2bMFHH30Eh8OB/v3741e/+lVMW8Pp06fj/fffx9atW7FmzRpYLBb07dsXP/rRj4zV6ubY7XY8+uijxoS8F198EQ6HA2PGjMH111+PMWPGpPQYM0Xfvn0xf/58vPDCC1i5ciXeeOMNSJKEgoICjBkzJqFvd1cQlM7eQmzSVCF/V9Cbi1PPx+c6O/B5zh58rrNDZzzP//nPfzBv3jz83//9H0455ZQOvW1qu3T+n26q44pZyivHiqJgxYoVePbZZ7Fjxw7U1taiuLgY48aNw0033dThjd2JiIiImnPkyBEUFhbGfG7Hjh1GB4jmxkgTxUs5HP/973/H008/jaKiIqNB+ddff42XX34ZS5YswYsvvtjtdksSERFR9/WPf/wDBw4cwMiRI+H1erFv3z589NFHiEQi+O1vfxszaY+oJSmF47KyMjzzzDPo168fFi9eHDO5Z968ebjvvvvw9NNPt6pnInW8uU/LkCQBM6YLCZfNm68gGlUw6wY2KCEiop7lnHPOwaJFi/D++++jrq4OLpcLY8eOxTXXXJMwypuoJSmF43379kGWZZxwwgkxwRgAzjrrLNx3330d2gicUiNJAuY8pZaQmwPyvPkK5jyl4MaZiaGZiIiou5s0aVKzGxmJUpFSOB44cCCsVivWr1+Purq6mID8wQcfAAD/QksjPRCbA7I5GCdbUSYiIiKiRimFY5/Ph5/85Cf4xz/+gdLSUpxzzjlwu9345ptv8Mknn+Cqq67Cdddd11nHSq1gDsjPPKsgHAaDMREREVErtamV2xtvvIHf//73xlQgABg7dizuvvtunHTSSU1+nSzLKTXiprYbc1I5wmHAagU2ri1I9+EQERERdQspd6t47LHH8Nhjj+FHP/oRLrnkEuTk5OCrr77C/fffj+nTp+PBBx/E+eefn/Rrk42B7CrZ1Cdz3nzFCMbhMPCvf1dk1cpxNj3X2YzPc/bgc50d+Dxnj0zvc5zSMu4nn3yCf//737j22mvxwx/+EMXFxXC5XDjxxBPxxBNPwG63s1NFmplrjP+3QsSNM9VNevPmd9msFyIiIqJuK6WVY33T3bhx4xIuy8/Px/Dhw7FhwwZUVFQYs9ip6yTbfJdskx4RERERJZdSOA6HwwDQZLs2/fM2m62dh0VtEY0m70qhfxyNKgAYjomIiIiaklJZhT5+cd68eaitrY25bNGiRdi1axdGjRqV0AOZusasG8QmV4ZnTBc4AISIiIioBSmtHE+aNAkvvvgiPv30U5x//vk455xzkJOTg61bt2LVqlWw2Wz4zW9+01nHSkRERETUqVJaSpQkCXPnzsXdd9+NPn36YOnSpZg/fz6+/fZbTJkyBQsWLGi2lRsRERFRay1ZsgTjx4/HkiVL0n0oAIDZs2dj/PjxWLduXcznx48fj1tvvTVNR0UdLeVWbjabDTfddBNuuummzjgeIiKiVkl1Iuvq1as76UiIqCdJORwTERFlglmzZiV8bu7cufB4PLjqqqvScETU0c466yyMHj0ahYWF6T6UZr344otwOBzpPgzqIAzHRETULSU7g6mHY57d7Bk8Hk+32OQ/aNCgdB8CdSCGYyIi6tH279+PSy+9FKWlpZg+fToef/xxbNy4EdXV1Vi4cCEAGJf//ve/T/j68ePHY+zYsXj88cdjPu/3+/H888/jvffew/79+2G1WjF69GjMmDEDY8aMadWx/fnPf8ayZcuwYMECrFy5EosXL8bevXtx3nnnGcdSUVGB+fPn46OPPsKhQ4fgcrkwduxY3HTTTRg8eHDCba5fvx5PPvkkvv76a9hsNpx88sn48Y9/jD/+8Y/YsGFDTHnJ7NmzMXfuXDz66KM4ePAgXn75ZezcuRMjR440Hm8qj/PIkSOYP38+Pv74Y5SVlcFut6OoqAjHH388br/9drjdbgBAXV2dcZuHDh2CKIro1asXRo4ciZtvvhm9e/cGoNYc//Wvf8U999yDKVOmxNzXF198gXnz5mHz5s0IBALo06cPJk6ciB/84AcJq7j6c3jvvffi0UcfxapVq1BfX48hQ4bgtttuw4knntiq56spyX5G9Od24cKF+Pjjj/HKK6/gwIEDyM/Px5QpUzBz5kyIYuLWr5UrV+Lll1/G1q1bEQwG0b9/f0yePBlXX301JElq13FS6zAcExFRVti7dy9uvPFGHHXUUSgtLUVNTQ2sVqvRwz8V1dXVuPXWW/Hdd99hzJgxGDduHPx+P1auXInbb78d9957L84888xW394DDzyAzZs349RTT8Wpp55qDNLau3cvbrvtNpSVlWHcuHE444wzUFlZif/9739Ys2YNHn74YYwePdq4nTVr1uCnP/0pLBYLzj33XBQWFmL9+vW45ZZb4PV6m7z/5557DuvWrcPpp5+O733ve0YIS+VxBgIB3HzzzThw4ADGjRuHM888E5FIBPv27cPSpUtx3XXXwe12Q1EU3HnnndiyZQuOO+44jB8/HqIoory8HB988AFKS0uNcNyU9957D7/73e9gtVoxceJE+Hw+fPbZZ5g7dy4+/fRTPProowkzF+rq6nDzzTfD7XbjggsuQEVFBd59913cddddmDdvXtI/NDrCI488gvXr1+PUU0/FuHHjsHLlSsyZMwfhcDhhE9/jjz+OZ555Br169cJZZ50Ft9uNjRs34uGHH8aWLVtw7733dsoxUiyGYyKiHuq1117Dfffdh7q6unQfSlIejwe/+c1vcPHFF3fJ/X3xxReYOXMmbr755pjP79+/P+XbeuCBB/Ddd98lrGj+8Ic/xMyZM3H//fdj/PjxsNvtrbq9b7/9FvPnz0dxcXHM5//0pz+hvLwcDz74YMx02htuuAEzZszAfffdh+eeew4AEI1Gcd9990FRFDz66KMxofkvf/kLli5d2uT9b9iwAXPnzsWQIUPa/Dg/++wz7N+/H1dffTXuuuuumNvx+/1GWN2+fTu2bNmCM888E3//+9+N6/h8Phw6dAiRSKTZ75Xf78d9990HSZIwe/ZsDB06FACgKAr+8Ic/YPny5fjvf/+LmTNnxnzdtm3bcNlll+FnP/uZsWJ70kkn4d5778Wrr76KX/7yl83eb1t9/fXX+O9//2vUTc+cORNXXHEFXnnlFdx4442wWq0A1D9snnnmGUyYMAH33XefsfqtKAr+8Y9/YNGiRXjvvfdwzjnndMpxUiNOhSAi6qEeeeQRbNu2DQcOHMjIt23btuHhhx/usu9HQUEBbrjhhnbfTlVVFd59912cdNJJCaf6CwoKcO2116KyshKfffZZq2/z2muvTQjGW7duxaZNm1BaWhoTjAFgwIABuPjii7F9+3Zs374dAPD555/j4MGDOP3002OCMQDccsstzZ6Sv/jiixOCcVsfZ7I/CNxutxECm7uezWaDy+Vq8jgBteygtrYWU6ZMMYIxAAiCgNtvvx2SJGHZsmUJX+d0OnH77bfHlDKUlpZCkiR8+eWXzd5ne8ycOTNmQ2FeXh5OP/101NfXY9euXcbnX331VQDAr371q5iyEP1xCYKAFStWdNpxUiOuHBMR9VB33HEH7r333oxeOb7jjju67P6GDh2aENDa4ssvv0Q0GkUoFMLs2bMTLt+zZw8AYNeuXTjttNNadZujRo1K+NzmzZsBqDXHye5HD1a7du3C4MGDsW3bNgDAcccdl3DdXr16oXfv3k2ukie7/1Qf59ixY1FQUID58+dj27ZtOOWUU3D88cdjyJAhEITG6a2DBg3C4MGDsXz5chw+fBhnnHEGxowZ0+rWfFu3bgXQOLXXrHfv3ujfvz927doFv99v1DgDQElJSULwtlgsyM/P79T/I8OHD0/4XK9evQAg5n43b94Mp9OJxYsXJ70du90eE6ap8zAcExH1UBdffHGXlSx0B3odb3vV1NQAUMs0vvjiiyav19DQ0OrbTHZs+v2sWrUKq1atavF+/H4/AHVlsqn7aCocN3f/rX2cHo8Hs2fPxpw5c/DRRx/h448/BqAGwenTp+Pyyy8HoAbSRx99FHPmzMH777+Phx56CIBaVnH55ZdjxowZza5y64+zqeczPz8/aTg2v28mSRKi0WiT99deye5Xf3zm+62pqUE0GsXcuXObvK1Ufqao7RiOiYgoq+mn2ZMFpGQrinrYueaaa/DjH/+4045Lv5+f/exnuOKKK1p9/aqqqqSXV1RUtOn+U3mcffv2xe9//3tEo1Fs374da9aswcsvv4z/9//+H3JycnD++ecDUAP83XffjZ/97GfYuXMn1q1bhwULFmD27NmwWCy4/vrrWzyuph6P/vmmwnCmcrvdEAQBb7/9droPJeux5piIiLKa3sWhrKws4TL9FL7ZyJEjIQgCNm3a1KnHpZc6tPZ+9PrbZKu8hw8fxqFDh1K6//Y8TkmSMGzYMPzgBz/AX/7yFwDAhx9+mHA9QRBw1FFH4fLLL8fTTz/d5PXM9DKF9evXJ1x2+PBh7Nu3D/369et24XjUqFGorq7G7t27030oWY/hmIiIsprb7caAAQPw+eefG3W0gHr6Pr63MaBuRjv33HOxadMm/Pe//4WiKAnX0XvvtseoUaMwatQorFixIulGLFmWYwLi8ccfj+LiYnz44YfYsmVLzHWfeOKJlEsHUn2c27dvx4EDBxKuo6/k6hvw9u/fjx07diRc78iRIzHXa8oZZ5wBj8eDpUuX4rvvvjM+rygKHn/8cUQiEUyePLmVjzJzXHnllQCAv/3tb6iurk64vLy8POn3jToeyyqIiCjrff/738ff//533HTTTTjnnHOgKAo++eQTjBgxIun1f/7zn2P37t145JFH8Oabb+LYY4+F2+3G4cOH8fXXX2PPnj1YunRpu0cK/+Uvf8Ftt92G3/3ud3jppZcwYsQI2Gw2HDp0CJs2bUJVVRVWrlwJQF2t/cUvfoGf//znuO222zBx4kQUFBRgw4YNKCsrw9ChQ/Htt9+mdP+pPM7PPvsMDz30EI477jgMHDgQubm52LdvHz766CPY7Xaj5njbtm345S9/iZEjR+Loo49GQUEBysrKsHLlSkiShGuuuabZY3K73fj1r3+N3//+95g1axYmTpyIvLw8rF27Fl999RVGjhyJa6+9tm3f8DSaMGECZs6ciaeeegqXX345xo8fj+LiYlRXV2Pv3r34/PPPccstt+Coo45K96H2eAzHRESU9aZNm4ZIJIKXXnoJixcvRmFhISZPnowbbrghaceJ3NxcPPnkk3j11Vfxzjvv4O2334YsyygoKMDQoUMxc+ZM5Obmtvu4+vbti/nz5+OFF17AypUr8cYbb0CSJBQUFGDMmDEJPW9POeUUPPTQQ3jyySfxzjvvwG634+STT8Zf//pX/PSnP0251CCVxzlu3DhcccUV2LBhA95//300NDSgqKgIEydOxHXXXWeEumOOOQbTp0/H+vXrsWrVKtTV1aGgoACnnnoqrrzyyqSdM+Kde+65KCgowDPPPIP333/fmJA3c+ZM/OAHP2h1f+lMc/PNN2PMmDF4+eWXsXbtWtTW1iI3Nxd9+/bFrFmzcMEFF6T7ELOCoCQ7T9JJKisru+quEvh8vrTeP3UdPtfZgc9z9uBz3X5+vx+lpaUYPHgwnnrqqXQfTlJ8nrNHOp9rn8/X4nVYc0xERNRDNDQ0GK3OdNFoFI888giCwWBKI62JshXLKoiIiHqIPXv24JZbbsG4cePQr18/1NfXY+PGjdixYweOPvpoY9MXETWN4ZiIiKiHKCoqwjnnnIMNGzZg9erViEaj6N27N6699lrMmDEDTqcz3YdIlPEYjomIiHoIn8+H3/3ud+k+DKJujTXHREREREQahmMiIiIiIg3DMRERERGRhuGYiIiIiEjDcExEREREpGE4JiIiIiLSMBwTEREREWkYjomIiIiINAzHREREREQahmMiIiIiIg3DMRERERGRhuGYiIiIiEjDcExEREREpGE4JiIiIiLSMBwTEREREWkYjomIiIiINAzHREREREQahmMiIiIiIg3DMRERERGRhuGYiIiIiEjDcExEREREpGE4JiIiIiLSMBwTEREREWkYjomIiIiINAzHREREREQahmMiIiIiIg3DMRERERGRhuGYiIiIiEjDcExEREREpGE4JiIiIiLSMBwTEREREWkYjomIiIiINAzHREREREQahmMiIiIiIg3DMRERERGRhuGYiIiIiEjDcExEREREpGE4JiIiIiLSMBwTEREREWkYjomIiIiINAzHREREREQahmMiIiIiIg3DMRERERGRhuGYiIiIiEjDcExEREREpGE4JiIiIiLSMBwTEREREWkYjomIiIiINAzHREREREQahmMiIiIiIg3DMRERERGRhuGYiIiIiEjDcExEREREpGE4JiIiIiLSMBwTEREREWkYjomIiIiINAzHREREREQahmMiIiIiIg3DMRERERGRhuGYiIiIiEjDcExEREREpGE4JiIiIiLSMBwTEREREWksbf3CFStW4Pnnn8eXX36JhoYGFBYWYsyYMfj5z3+OPn36dOQxEhERERF1iZTDsaIo+MMf/oCXXnoJAwYMQGlpKdxuNw4fPozPPvsM+/btYzjOQnOfliFJAmZMFxIumzdfQTSqYNYNPFFBREREmS3lcPzss8/ipZdewrXXXovf/va3kCQp5vJIJNJhB0fdhyQJmPOUAgAxAXnefAVznlJw48zE0ExERESUaVIKx4FAAI8++ihKSkrwm9/8JiEYA4DF0uZKDerG9EBsDsjmYJxsRZmIiIgo06SUZFetWoWqqipMmzYNsixj+fLl2LlzJ7xeL0455RQMHDiws46TugFzQH7mWQXhMBiMiYiIqFtJKRxv3rwZACBJEqZOnYodO3YYl4miiBkzZuCXv/xlk1+fm5sLUUxf3anP50vbfWeLn9wJPPNsOcJhwGoFfnJnflqOg891duDznD34XGcHPs/ZI5Of65TCcXl5OQDg6aefxsiRI/HKK69g8ODB+Oqrr/C73/0OTz31FEpKSnDNNdck/frq6ur2H3Eb+Xw+VFZWpu3+s8W8+YoRjMNh4F//rujylWM+19mBz3P24HOdHfg8Z490PtetCeUpLeMqilpParVa8eijj+K4446D2+3GSSedhIceegiiKOLpp59u29FSt2euMf7fChE3zlQ36c2br6T70IiIiIhaJaWVY4/HAwAYPXo0evfuHXPZ0KFDUVJSgl27dqGmpgY5OTkdd5SU8ZJtvku2SY+IiIgok6UUjo8++mgAgNfrTXq5/vlAIMBwnGWi0eRdKfSPo1EFAMMxERERZbaUwvG4ceMAAN99913CZeFwGLt374bL5UJ+fno2YVH6NDfgQw3IDMZERESU+VKqOR4wYABOO+007Nq1C6+88krMZU8++SRqamowceJE9jomIiIiom4p5RT7hz/8AVdffTXuuecevPPOOzj66KPx5ZdfYvXq1ejXrx9+8YtfdMZxEhERERF1upSbDg8YMAALFizApZdeii1btuDZZ5/Frl27cO211+KVV15BUVFRZxwnEREREVGna1P9Q58+fXDfffd19LEQEREREaVV+sbVERERERFlGIZjIiIiIiINwzERERERkYbhmIiIiIhIw3BMRERERKRhOCYiIiIi0jAcExERERFpGI6JiIiIiDQMx0REREREGoZjIiIiIiINwzERERERkYbhmIiIiIhIw3BMRERERKRhOCYiIiIi0jAcExERERFpGI6JiIiIiDQMx0REREREGoZjIiIiIiINwzERERERkYbhmIiIiIhIw3BMRERERKRhOCYiIiIi0jAcExERERFpGI6JiIiIiDQMx0REREREGoZjIiIiIiINwzERERERkYbhmIiIiIhIw3BMRERERKRhOCYiIiIi0jAcExERERFpGI6JiIiIiDQMx0REREREGoZjIiIiIiINwzERERERkYbhmIiIiIhIw3BMRERERKRhOCYiIiIi0jAcExERERFpGI6JiIiIiDQMx0REREREGoZjIiIiIiINwzERERERkYbhmIiIiIhIw3BMRERERKRhOCYiIiIi0jAcExERERFpGI6JiIiIiDQMx0REREREGoZjIiIiIiINwzERERERkYbhmIiIiIhIw3BMRERERKRhOCYiIiIi0jAcExERERFpGI6JiIiIiDQMx0REREREGoZjIiIiIiINwzERERERkYbhmIiIiIhIw3BMRERERKRhOCYiIiIi0jAcExERERFpGI6JiIiIiDQMx0REREREGoZjIiIiIiINwzERERERkYbhmIiIiIhIw3BMRERERKRhOCYiIiIi0jAcExERERFpGI6JiIiIiDQMx0REREREGoZjIiIiIiINwzERERERkYbhmIiIiIhIw3BMRERERKRhOCYiIiIi0jAcExERERFpGI6JiIiIiDTtDsezZ8/G8OHDMXz4cGzcuLEDDomIiIiIKD3aFY63b9+Ohx56CC6Xq6OOh4iIiIgobdocjqPRKH75y19ixIgRmDhxYkceExERERFRWrQ5HM+ePRtff/017r33XkiS1JHHRERERESUFm0Kx9988w0eeeQR3HrrrRg6dGhHHxMRERERUVqkHI4jkQh+9atfYfDgwbj55ps745iIiIiIiNLCkuoX/Oc//8HWrVvx8ssvw2q1pvS1ubm5EMX0dY/z+Xxpu2/qWnyuswOf5+zB5zo78HnOHpn8XKcUjr/++mv85z//wcyZMzFq1KiU76y6ujrlr+koPp8PlZWVabt/6jp8rrMDn+fswec6O/B5zh7pfK5bE8pTWsb95S9/iZKSEtxxxx1tPigiIiIiokyV8soxABx77LFJL7/qqqsAAI8++ijbuxERERFRt5NSOL788suTfn7t2rXYuXMnzjnnHOTn56Nfv34dcnBERERE1P0oigI5GITc0IBofT2i2r9yQwPCTiekkSMhWlLe+tYlUjqqv/3tb0k//6tf/Qo7d+7ELbfcgjFjxnTEcRERERFRBlEUBUo4rIbdQAByfX1M8I3W1yNSXY1ITQ0itbWIBoNQwmEokQjkcBiQZSiyDHdhIYr79IG9qCjdDympzIzsRERERBlg7tMyJEnAjOlCwmXz5iuIRhXMuiF9nbg6ghyJJKzw6qu8kfp6RGprjdArBwKQw2Eo4TDkSASIRACh8XsjWCzqm9UK0WqF6PFAsFggWq0QJAnR+noo9fVpfLQtYzgmIiIiaoIkCZjzlAIAMQF53nwFc55ScOPMxNCcCRRZRrShoTH0xpU2RGprEdYCb7S+Xg272iqvogdeRX3ckCQ13GqhV3K5jPcFSYIgZOb3oK06JBzff//9uP/++zvipoiIiIgyhh6IzQHZHIyTrSh3Fr2ON1pfr5Y0xK/21tUhXFOjBt66OsihUGPgDYfVGxEEQJYBSWpc0bVaITockDweNfBaLD0u8KaCK8dEREREzTAH5GeeVRAOo0ODsazX8TY0JNbx+v2I1NQgXF2NaF1dYx2vttILRYlZ5RX0sKv9a3W5GgNvGgexdScMx0REREQtmDFdMIKx1YoWg7ESjSbU75pDr75pLVJdrYbiSARKKNR0Ha8eei0WiB5PY5mDJHX2Q886DMdERERELZg3Xw/GCsJhAXMersL3J5UlljVUV6ub1/z+xjperbQhpo5XFI3VXcFqheRwQPB6e2wdb3fCcExERERZT4lEEPH7Ea2tRaSuDpG6OkT9fkT9frz4Xj+8vPZYXDpsFS4auBKvfzsB8xachco1azCl77sxtyPYbBD1lV6bDVa3u3Hll4G3W2A4JiIioqygKAqifj9CZWUIV1QgXFOD0JEjCB05orYpC4XU0oZg0ChrWLL3bLy+71hcMvA9TBmwGoJkwbTRGyA5HFjw1Xmw+nyYNnpDmh8ZdSSGYyIiIupR9DZm0fp6RKqqECovR6isDA179iBcUaG2LotE1CuLIkS7HaLdrpY25ORAtNmMzWuSvwCX56/FtNHbATQOrbh0zCYIFgtkhavBPQ3DMREREWUMYyOb32/06ZUjESjRqNGD1/wW1UcUB4PqgIpAAFG/32hjJgcCRkcH0eGA5HLB3qcPRJutVcdz2bHrm7yMK8Y9E8MxERERdSpFUdQRwoFA49hhUwCO1tejKhRC9b59iFRXN/bn1d6Mzg36v9qmNkVR1DpeUVQ3sUkSBFE0anytLhfEXr0gWBh3qPX400JERJSlFFk2uixEtM1nciAAORhUh03oXRi0FVklHIYcCjV2XBAENZDqfXUlSQ2wogjIsnF9WavjVSIRdRVY795gYnc6EVYUtaRB38jGgRSUBgzHREREPYwSiTSODDa/NTQg2tCASHU1wlVVjau02htkObbdGNQeuxBFdUVWktTgG3NnChRZVr822YquIBjT2AS7HVaPJ2n3BqfTiYaGhi75/hA1h+GYiIiom9BDr77KG/X7G6eo6T12a2oQTdZjVxQbp6hp4VQ0tRsTbTY1xHKVlrIcwzEREVEGkEOhxtVdv98odYjU1SFSWYlQZSUiNTVqqzGtJhey3HgDghAzNlh0OCB5PBBsNg6VIEoBwzEREVEH0rstyIFA479aza5ey2sEYdObHAgYK70xdb3QVnptNoh66PV61drcVowOXrDpBIiCkrSzwqLNYyErQrMdGYiyDcMxERFRCvRBEpGqKrWMobYW4epqhI8cMT42Shq0dmPmoGvQuyroXRasVkhOZ2Of3VYE39YQBQWvbjoJQGzrsUWbx+LVTSfh8mPXdsj9EPUUDMdERERJKLKMSG2tGoIrKxGuqkLw0CEEDx5EpLZWXekNhYzrm1d3BZsNVperceNZ/Ca2LqQHYnNANgdj9uolisVwTEREWUWORBr77JrLHvSJarW1ahguL0dEu1zRQrBgsUB0OCA6HLB6vRDt9m5Ry2sOyK9tGYuILDEYEzWB4ZiIiHoUJRIxSh0iWveGcFWV8RbTyUEvezDTN7Zp44SteXkJbce6o2mjNxjB2CJGGYw7QDrruVlL3nkYjomIqFuJBgKIVFfHtDCL1terIbiyEqGyMnVFWBs6AaDpTg5ZNGRi0ebGYByRJSzaPJYBuZ3SWc/NWvLOw3BMREQZSYlGEa6sRPWBA6jcsQPBsjIE9u9HuLJSDb6hEJRotPELBAGizaau+LrdsBYUZE3wbUl8jbH+MQAG5HZIZz03a8k7D8MxERGlXTQQQLi8HCHtLbB/P4L79yPq90OKRhEKBtXwq9f75uWxf28rJQtMyYIVtU0667lZS945GI6JiKhTKYqi1vgGg419ff1+tf1ZRQUCBw4gXF6u9voNBgFFUUsfXC5IXi88+fkImLpCUGpkRUgamPSPZYV/XLRXOuu5WUve8RiOiYgoJUokgqhW1hDVB1sEAjEDLSJ1dYjU1hrjjfURxsY4Y70cQhAg2u0QnU5YCwuTdn/oqH6/2aq5TVkMUh0jnfXcrCXveAzHRERZRJHlxpHDgqCu6kYiUKJRKOFw4yS3hgZE/H713/p6teuDNuBC1mp99U4P+tfH0AdcWCwQLRZAkjjOmHqkjqjnbmvnCdaSdw6GYyKibk4fVxzTvaGuTi1dqKlROzv4/ZBDIcjhcOy0NkWBoiiALEOR5ZjAa6ZPcNMDr97vV5Ckxs8x7FI31paA2lH13E11nvjru5Px1eG+STtP/O3dUnx5uB9ryTsBwzERUZopitJYmhAIQAkG1SCrhVnF/H443FjCYArE5usqkQigB1VRVNuXWSzqaq4oNl6mEURRXdk1B12GXcoybWmN1lH13E11nvjqcN+k11+0eSy+PNwPI3vtYy15J2A4JqIeRVGUxlrYUCgmaBo1r+ZSAEVRSw30f2VZXUmNRiFr15MjkcY6Wf16gFqeoK+4am+IRtUQKkkQ9XHCdru6ymqxqF+jKJBDIXWFV6vJlUMh4z6MY5PlxiArCOqKr6IYt2+86eOK3W6WLBC1UVtao3VkPXdTnSdSPaa23DfFYjgmom5DDocRqalB1O+HsHcvqg4eVMOl1vkgUlOjlhMEgzEhU4lG1dCqKAmrpkbo1MVfR1tpFQRB/bzpMsH8sfa+AEDRb0cP0tGoEcDNt2uuyRUsFohut/o5bQXXuF8i6hLpbo3WXOcJtmvrOgzHRJQR5EjE2ASmr6ZG6+oQqatDuKICoSNHEKmpMVaBLQDC4bDx9YLFYtTEino9rBY0IUkQ9JICIqJmpLM1WlOdJ7pLu7aYfQvhcONZN/0MXCiESG0thFAIvRsa0n24TWI4JqIuoUSjxnjfcFUVIrW1iNTUIFRRYYwCVsJhyNobtLpZRVHUmlmbDaLNBsnjgdVmgysnB4FAIN0Pi4h6mHS1Rmuu8wSAtByTuQQtoSxNC7yyVrqmBIOQI5GYUjPEnzHTblMQBETq6zv9+NuK4ZiIOoQciTSu+Gqrv5G6OkSqqxE8fBjhI0cQqa+H3NAQ0+NWsFrV8Gu1qq2+vF51BbiFulmWGxBljra2Iss06WqN1pquF+05JmNF11xuZm7FGIlAjkYbN/+a90CY9lYYbSDN9LNy+r+SBNFma/xc3Gt1pL4eit/f1m9Vl2A4JqIWKbKMiNYSTG8TFvH7EamtVVeBtVpfo5tCOBzzIirYbGrwdblgzc9nJwSiHqYtnR4yTTrHbDfV9UJ3TK99uOSYtZBDUUwd/DHkUAivbjoF0fp6TB30obpiG42qAVcvadA73eibifXNxs0FXUEwQq4ebkWrNTYAZ8FrN8MxEQFQA7AcCkEOBBCprka4qgrhykoEDx9GYN8+dfhDMAjFVOcbv/IrOZ0QcnPVjznVjDrAgk0nwGaz4KLhnyZc1p1WJHu6tnR6yDSdNmZbLzPQNgcbm3RNb5Pz34ASjaJ+Z2zNbv2BPpjiew2TnK+j8pPGbjpnyasRcO9FwwEBNdWfN24M1ksYTCHXCLSSBNG8wssNv01iOCbqRvQ2ZRG9fKG+Xq330t7MnRn0lQHZ/EKsn1rTN0pEIsbpMzkQaPycOQSLIiSXC5LTCavPp5Y88AWVuogoKHhx/fGIhMPddkUyWzTX6SEhEGr1qvprlSLLkK1WhILBxBvWO8GYgp3exjDmOqa2jDHiB91o9x9zPUHAZN9eQBQRPCjGfF4QRUwuXgEIAkJljauuiunYoT+mJOUKRqtI7RhijtMcZrVjNT4WRUyyPg+IIpSI+rE54E52r9CCb347nzmKx3BMlGZyJAJZC7rGUIf6ejWsBoOINjSotbtaCzM5rm9v/Au8/iIsaJvZ4luQGUMgzL9sBMHo7CC6XLDm5an9chmCKc2mjd4Ai9WKF9d33xXJnk4OhyFrr12Tcl7Ha8IYRGQLLEIYZ/v/g8qPo7G9xE09xc2vX5IkIRqNJrZbBBIDr2mYjX5tJdn19M8l+3wy8a0dm7ss2cf6a6sWbs3vi/rl+kqu1j2Hr7OZh+GYqBNFAwGjK4O+Sc080jdSW6sGYa1WV295E7OKoAdXU6syyeOBVStlYHsy6umuHLMJkXCYfV4zgBwIxExmDNfUQG5oUPcZRKN4u/4yRBQLJIQRUaxYWjYJF+a8boRCUZKarF+1WCyIxI0tT0bRw66pZlaBKWQmC5t6kG5jEFVMIZhhtudjOCZqg/hxv8bKb3292p7syBGEjhxRf3FoK716azIoitp312JprNV1OCC0sksDUTbqLn1euzOjpErvSav1pZXDYTUQ19YiqpVh6dMb9T/cLW433qy6CMvqL8aUgsUoLViGZeWlWFJ+OUSbDaUFyzrsOAXTCqzxuQ679Wbuk7IGwzGRiRwMqqu5WhuyaEODerowEFA/V1trjPzVyxr0Gl6jPRnUgRSiNjbYmpsLwW5n6CVqh3T1nu2RFEV9TdP/qNde7/Q2i/ElDwrUcizjD3qHI2HD7bLyUiypmGoEYwDGv0vKp8Z8TD3XkiNTIApy0ud6WXkpAuEQjlGeRVFry1zShOGYskbMZjY96NbUqCu95eXqBLbaWqPPoxJ/es807teYwuZyNZY7MPwSdYqXNx6LVzcd3+W9Z7s7vfuMvmE32tBg9CLXS7niS7dEh6NNLbtkRYwJxjr9Y1np+vKvloKarIiYUriky4+rJxMFGW8cuQg1gQoMsbyO3bW12F1bi4/KfKhquAeR8H4AgEUQsHzXLowZMQLz5iuIRhXMuiFzSgQZjqlbUiIRNeRq44XNG9jqLRbUVlaqvxC0LgzRQECti9M3s2n9H3WCxQLRbodgs0HyemG12diVgSgDqEH4+LT0nu0uFFmO2dQbqatDtLZWfa3TOkIYJEn9w95qheByddieheZCZrpWjEVBTrpqrZZ7qKvc1HbBaBR7tfCrv+2pfQc7am/FV9EkXUdMIoqC8spKzJuvYM5TCm6cmVm/axmOKePI4bAxZCKqlTBE6+sRqa9HpKrKGDdsNDgPhWJ2DNtsNoTCYaMbgyBJao2vKKr1vdzMRtRtyIqAq0/4HBcN7+Des92UIstGZ4hofT3CNTWI1tQ0lnlBrY81Nu9mcUlXsrIOczBmmYequRX2pUcuRF2oDsOtC9UAXFNjBOFD9fVIpTjCYXFDsI3CYK8VlxZUYtves/HfJWownjE9s34+BUXpusKPysrKrrqrBD6fL633TyolGlVLGvTODfqktbo6NfiWlyOib2KLW90FoL7I2+1qPa/Vqk5e08dUapxOJxoaGrr6oVEX4/OcPbL2uVaUxlIIrTNEtLa2sbsN1FpgUT/T1c0nT7a2W0Wq9EBsEdQOGgzGsZaVl+KNskk4xfUUBklLjfD76RE3qhv2QpZrWn1bIoA+Hg8GeL3YFrkYVtswuBxH44GRc5FntxvPhYQworCmJRj7fL4Wr8OVY2oXJRpVN60FAjFDJJRIxChliNbXI1xdjVBZGSLV1YgGg0lXfM3BV3K7G0sbuLpLRFnAWDzQ+pqHq6ogBwIxA3lEq1UtAfN4unUQ7kqlBcvwVsWFiChWWIRwVgfj6mBQK38wl0O8hX3+enylJBkn3QRR9KK3uxDH+qIo8XoxMCcHA7xe9HW7YZMkLCsvRbXpD5KP6ypQal+G0oJleLP8QkRhhcUiY8b0zIyhmXlUlBEURVFP3el1vdpKb7i2trG8oabG6M1rnnZk9J/UX7y11Q3RblfbluXkcMQwEWU1ORxGVOuAE66qUs+ahUJqjbA+mp1BuN2WlZcawTiiWLGsvLRHB+SILOOg3x9TC6wH4uq4s7HNE5DrKEDEchxG5Ik4o6gc+5WJWB+8Hpf0XoPJhW8m/ar40hX9Y10UVrUPdsSKefOVjCupABiOs5pR21tXp/5repEOa3W90UDAmMaGuFZlgtVqnM4TXS5YLRajtpcz24mIYinRqPpaW1ODUGWlunciFFIXE7QFBMntztoa4c7QXFDr7gG5LhxuXAHWaoH31NVhb20tIilUzDokCSVeLwZ4vdgcuhoW+zC4HEfh4ZGPwGGxGN+zd2X1j4tpxYtRWtC6YAwkqf3OWYALpOex9rQnMOepQgDIuIDMcNxD6UMqzKE3WluLcG0twhUVavjVVilkvam7Tq9h0+p6rS6XOkqYL9hERK2iyLJRbhZtaEC4uhqRqipEAwEo0ahaK2y3w+L18gxaJ2lVUMvwgCwrCg7V18es/urvVwQCKd1WodOJAR4PBmglECUeDwbm5KDQ6YQoCFhWXooDplKI96qnorRgWUplKU219NMNdW7FpJzXofiBayZXwF5UhDlPqUE+kwIyw3E3lRB+9TetZ2+4vBwRv1+t7dUmHhnjMy0WYyOb5HbD6vOp4ZfBl4goKXPYlbWhP0o0apSSKdFoTAcdJRxW92CYegl3l5XhntIfOBN7LzelPhIx2qLtiSuFCMmtrwW2iiL6axvi9NVg/X231drk17VUCtHaspSmfi7Mz0WkvvHzeiCORhV0/pzD1mM4zmByOGwEXv1UXLi2FuEjR9SuDnV1ycOvVqcmWq0Qc3LUjW3dfBczEVFXUiIRY9EhXFmJaF2dGn4jkcaNxPo4eJ0oNpaVSZJ6Bq4Dewl3lZ7SHzjTei8rioKyhoYkG+JqUZZiNxaf3Z4Qfgd4vSh2uyGl+Lu+NSvs7S1Lae65UANyZuUThuM0UhRF3ZmsTWkzVn4rKtRpbdXVxmQj87Q2vdZXtNkYfomIOoAiy+rmuNpadd9FVZX62ivLRrs00W6H4HZ3u7CbKvYHbp9gNIp9dXUJfYH31NWhIYVWdZIgoK+2CjwgLgjn2GwddrytKYXormUpbcVw3MnkSKQx/GpveluzcHm52gZNm9pmrEBotWii3a4OrMjP57Q2IqIOFNM2rbpaXR0OBNSNx1oYzuZ6YHMI0utNGYwbKYqCymAwoQRid20tDvj9KQ3H8FqtavDVa4G1euB+Hg8sXfCHWGtKIcwysSylozEcdwA5GETYHICrq9XV37IyhPUxxsGgWnsmCDEtekS7HVavN2GQBRERdQwlEjE2xkXr69WzdFqnCL0kTegm9cBdif2BgbAsY7++ChwXguvMG9lbIAIodruTrgLn2e0Z+TOXaWUpXYnhuJXkYFDdbayF37C28S106JBaE6y1PDPanQmCGn4dDnXTG1d/iYg6nixDDocbO++EQo0fBwKI1terixPRaOxUOasVotPJkrRmZFN/4JpQCLtrarCnri6mFGKf3w85hbZoLoslYTPcAK8XfT0e2LP0LER3xHBsIofDavCtrjb+TQjAwWDjgAtRhOhwqKu/ubnqdDcLv6VElGaK0jiUR3+TZbV0S1ES3tcH98T8CzT2KxdFdUXV1MfceNPuz3zfSSUJoMaxaVM1jbNs0ah6bIoCQRRRb7cjqiiAJBm3b1w/FFKPV+8eEb9BzmJRN8c5HBymkYKe2B84Iss4WF+PBXtHoLJhP9zyZ0YgrgoGU7qt3i5X0lXgAoeDP2M9QNYlOUVR1OBbVWUE4HBFBYKHDiFcUaG2RwsE1ACsvRibA7Bot0NgACaiNNBbhkFvG6a3CwuFEA0G1XHtgQAUbSOZEXa1IGwEx2QBNr7zQmsub+lrmnssSLI/XQ/icSVmit+PSPwpbK0jhCCK6qKE3c6SiA7S3fsD68Mx4jtC7KurQ1iWAbzVqtuxm4ZjmFeDSzweOJgDerSsenbrvvoKFatWIXDgAOSGhsYOEIJgBGDJ64W1qIgrwETUqZRIpLEvrtYiTIlEjNVUPfwa19MuM1Z+9aAcv1Kqr+5Kkvo6pq/+xq32tjdEKklCcXO3GX/9VO7fYrFASGGXP7VPd9iIpQ/HSLYhrjzV4RgOB1yOQaiVJmCsL4ALi/egxOtFL5cLYgf/sdVTekg3JxCJYL/fj8pAAJXBICoDAVRo/1YFg5jSrx/GeTzpPsxmZVUCrP3yS9Ru2gR7v36w5uWxBpiI2k2JRBLqXY0BEVqA1VdxFW2V1xx29ZKABPrmXb2MQRSNEgfRYontqZuG17FU7zPbX2u7UyjKpI1YDabhGOa3vXV1CCb7f9MEqyiiX1xbtD3yJHwamAm7xYGIYsXVxh8ExZ32eNLZQ7o9P4MNkQj21tXFBl7t/apgEJcMHoxT+/YFAHxx5Ah+8dFHTR7H6NxchuOMoigQnU5Yc3PTfSRE3d6CTSdAFBRMG70h4bJFm8dCVgRcduz6NBxZxzM2d+mtF7WNXlHtDJQ5DCdlWrUVRNEItqJWCmAEX+qxespgjc6gKAqOBALY5/djR1VVzKa4wykOx8i12TAwJydhQ1xvlytJW7Sv8Pk2R5d240hnD+n4n8H6SAS7a2qwouxYfFxZi6G2ldix93NUaeF32pAhOL1fPwDA5iNH8PNmAu+YoiIjHOc7HMix2ZDvcMBnt8On/6u9P9zl6rTH2FGyKxwTUYcRBQWvbjoJAGIC8qLNY/HqppNw+bFr03VobaLIsjH6Vw4G1bZffj8itbVqIA6HY1d49Q1qksSQSy3iYA0gFI1ir6ktmrkkIpXhGKIgoJ+5LVpODko8HpR4vci121t9O+nqxtGZPaTrw2HsqKkxVneNld5gEJWB9zGseB2WlP8JANAr8jTu/vBDAO8BAA7E3daJvXsb7+tBV/83z+FAvin4HpOfb1x3SF4eFk+diqZE6uuh+P3tfqydieGYiNpED8TmgGwOxslWlNPBCL36Bra4f6OBAGStFaOxAmxqyShYLBCsVljcbjUQM/xSG2XDYA1FUVAVNxxDfzvo96OJcytJefThGHEb4vp6PLC2cy5AurtxpNJD2h8OY3t1dUxJg/nfy4cOxVn9+wMAvqyo0AJvcif3fh/DChZjSflURAJHwWK9BgV2Gwa6A/CZA6/DgeE+n/F1g/PysOiiizruG5DhGI6JqM3MAfm1LWMRkaUuC8ZyJKKWNcRvWtOCr1EGoYXemA1s5i4L2gY2QZIgWq0QHA6GYOo0PWWwRkSWsd/vjxmRrAfi2jYMxyjxejEoNxf9TSvCnTUcIxO6cSw6dBaqa9dAiRxEMFKBX1cFkC9uMVZ7rxg2DOeUlAAAvq6owM+aCbzjihtrpAudTvR2uWLKGczlDcPy8tDfq/4MwnEsRo5cj4eG3tGpj7U7YjgmonaZNnqDEYwtYrTDg7EcCqmDHAIBRAMBRP1+RP1+iNEowqbgm9BSzNSbV7RaG0NwJ02i7E4brih9uttgjZpQKOkq8P66OrX3dCs5mxiO0c80HMNisSDSBV1JOqsbR20ohK2VlagMBrGqfDAawlXwCV8aq7xXDRuGcwcMwIN77sKGssPY9d0lxtceirutvXV1xvuFTif6ut2NgTeupGFIXp5x3UE5OXiptLTZ4+xuP4PpwHBMRO2yaHNjMI7IEhZtHtvmgKwHYT0Ah6ur1ZIHrQOEABihV7TbG8euZ8BKLzdcUUvSfSq/KVFFwUFtFTg+CLdlOEaJx4MBOTkxITiThmOk0o2jJhTCVxUVxia1iriShquGDcP5AwcCAL6tqjKVNHyacNv76urw4J678E3DCAzx7ILs8RgBtwbDsTfyPYzN248zCr7FYFPjgIE5OXj+wgvb/8CRuT+DmYbhmIjaLL7GWP8YQNMBWVEauz9o9b7R+np145sWhCHLsfW+Hk/CZjfJYmnsVZ4BevqGK66Mt08mnMr3a8Mx4leBG4djtI5NFFGirQIPNAXg/l4vnN1gRkB1MIgt5eUxIbdC68FbGQzimuHDjcC7vaoKv2ymS8NB08ayAqcTg3JyjBXeamU49kTG44S8fTiz4BvslC/GN/4RGOb8GneVLAKGTYq5rWXlwyArI3BaYX2nPO5M+BnsLjL/p5iIMlKyzXfmGmQ5HMbFR68yRvxGg0FE6+oQra83Jrsl3fjmcKidH7qhnrzhiivj7dNVgzVkRcHhJoZjHElxOEa+w2GUQgw0lUT07oThGO1VFQxi05EjSTesVQYCuGbECFw4aBAAYEdNDX7z8cdN3tYBU+AtcjoxODc3sYZXe39QTo5x3QFeL+adf37MbS0rPxpLyu/CC3XhFl8POvt1ojsMd8kUDMdE1HqyrI4rDocRbghi2tEf4MK891D/Xcjo/3tW4BM05ExG/V6gqnJdYvsziwWixQKL3Z4R5RAdradsuIrX01fGO1tHD9YIRCJqP2BtQ5z+/p7a2pSGY1gEAf1NY5H1cogSrxceqzXl42ov8xmKqmAQG8vKjJD7eXUv+EO1sMs7URkM4toRIzD5qKMAALtqavC7Tz5p8nbNK7yFTieG5eU19t+Nq+EdYAq8/b1ezD3vvDY/nkx6Pcik4S6ZjuGYiAx6uYMcDBorvnqbM6PXrzbt7ZzoakCWUVejfbEgqCu+koRJuYu1zXCN5RBLjkyBqMgoze3Zp+V78maXnrwynokURUFFIJBQBrG7thaH6lM79Z5rsyVuiMvJQXHS4RidpyoYxLrDh5P04FXfH1Nixx77AwCAfvIz+OPq1aav/irmtg6bvgdFTieO8fmMDWvxXRpKTBPZ+ns8eHLixE59nLqe/HrQkzEcE2UTRTFWfo3Aa675DQbV1mjmlSc99OqdHiSpcSNcCkMvsuG0fDZsdsmklbCeIhSNYp9p5dccgutTqKsXICLPWYRj8sSEcohVddM67Q/QikAAaw8darKkYfrIkZh69NEAgN21tfjLmjVN3lZv8VMcr/XhPc1VhtEFmxEUBuKIfBx6OUUMcIdxesG38Nnt6GcKvBuDV2Ly8Vdn1B/Y2fB60FMxHBOlg6I09uXV25ApSkz7MUGSGscNKwoURTF69eoji42BFqFQY+DVbldvbRbzdbIc+36Sml/R7Vbvv4PLHbritHw6N41ly2YXroS1jaIoqA6FjJ7A7RmO4bZaY2qA9bcvgpfjzcpLcVrc/6e2/AFaEQhgzcGDSVd3KwMBzBg5EhcPHgxAbTt272efNXlbR0wjoIucThxfWJi0pKHQ7UZvhwN5dv3/zSxY+k+HVbHiJu3Yl5RPRZ1jMc7I8D+ws+X1oKdiONYs2HQCREFJusN+0eaxkBUBlx27Pg1HRt2NHA5D0UsSTOHVWKk1jSJWTP15FUVRA6m+Gmt+U68QG5K1oBvT3zf+682fFwTj9kWLJS3jjjv7tHw6V6ezYbMLV8IaNfWHWESW8cK+E1HuP4Tewv9ihmSkMhxDgDocI3463ACvF74mhmMMxHJIoiXmOVl65EIsrVCfs3HuhViy40CTk9ZmjByJS4cMAaC2Hfv72qZHwJsDby+nEycUFcUGXtP7xS6Xcd0+bjf+fdZZSW/T3Oe4uTMU3aHuPRteD3oyhmONKChJW1CZd+QTAVA3pYVCjWOHg0H1/YaGxolt+hjiZMFVG0YBfTiFHlyhrfIqSuxqsn4berDVbyfFsoZM0Zmn5dO5aaynb3bhSlisUKQWiw8MxaYDOchTVhklEXvr6iErC1t9Ow5JSugJXOLxoL/XawzHiCcrCvT/9eUNDfho/35TyP0ENXX34cGvo/h/kTIUFY/F9cPV52zzkTr8v3XrmjyWClM3i14uF07u3bvJSWu9TYG32O3G/515Zqsfc2s0dYaiu9S99/TXg57e2pHhWGNuQaV/nKxVFWUHJRKJXenV+/L6/eq0tkjEKInQf0kJFovafUGvydXLIlIIr90r5rZNZ5+W7y6/PLubjloJ606/VKOKgkP6iOS4euDK4KsAgJ2tvK0ipzMmAOurwUVOp3Ff+sa4Iw0NWLpjByq13rsVcau8N44ejcuHDgUAHKyvx782NP37SYkcQmmBenkvlwvji4ub7NJQZAq8vV0u/PP001P8jnWMls5QsO49/Xr6HhKGYxNzQNbH4TIYZyYlElFDqim8KlpgbRBFhIPBxjIE44uUmNICfZSwIElQFMWo5dVv01j9NTXHF7RyBNFqheB0dsuV23TqqtPy/OXZ8TpqJSwTf6nWh8NJA/DeFIdjCIIdha4ijPLBWP0dlJODEq8X/nAY7+/di8pAANuqqtR6XlPovfnYY3GFFngP1dfjoY0bm7yfyrgV3lP79IkJvDvDE/B5w4WwW/MgWEqwrPx/KC1Yhl4uF+4/7bQ2f5+6QmvOUABg3Xua9fTWjgzHcaaN3mAEY4sYZTBOI331VgmHEdVDcEMDIrW16iAJLQzHEEVIFgui0WizoVWJL1kAGssbRFHtxWu3q6vBKa7+UnJdeVqem8YyV7p+qcqKgrKGhthuEDU12F1XF1M/2xr5WmuwIqcT9ZEINvvHQoEAWa5DruVzbDoSwIf79uGHxx6L4T4fAGBndTUe/fzzJm/THHh7u1w4o1+/pCUNeQ4HChwO47pFTif+duqpxsfLykvxbflUXDVwMUoL5ne7uvCWzlBsrR+ObQ3DWfeeAXryWTqG4ziLNjcG44gsYdHmsQzIqdDqZfV6W712Nr6GVtFDqT5UQm8vFgggqtfuah0Zkq7eWq0QXa6kXRXMmzrSqanTx0uOTMG3DUMwxPltwmpcpp1W7khdtUGFm8YyX2f+Ug1Go3huz1hU1u9HAVYaq8F7amsRSGE4hgDAabHAqpU6hKJRNESjmDVqFH5wzDEAgK8qKnDre+8BOGB83bem26gIBo33e7tcOLt//4SShjzTBjZdodOJP0+YkPJj7wl14S299pmDMdD9Hl9X6MrSpZ56lo7h2CS+xlj/GEBWBGSjRZgeSs3v6yUHWohNaAumv5k6KCjmlVlziYN5tTbJ6q0+SEIQRXX1Ng1dFTpCU6ePv20Ygm8aRiRcv6fUajWlKzao9IRwkC3a80s12XAMfUX4UH09FCxK6ViKXS6c0KsXBni9EAUBj33xBRQgaY/helPHiU2Bi5CT58MwTy1OyNuPPZHvYXPgPJxd+BWm9FoLnynwFjid+MP48a0+prYEnJ7eIaGnP76O0pWlSz31LB3DsSbZ5rtkm/S6g6ZCrhz/sak3rnHd5tqE6eJajOk1vEb5gbmrgrmlWHx5grm9WA/U1OnjbxpGYJjza3zTMMJ4IelJtVrplK2/PLvTJjdda36phmUZ++rqsNfvx7aKCuytq8N+bViGP4WzQ6IgQE72WqY5q39//PC44wCoHRu2V1fHlDQY7zscyLXZjON/v24qfjg2VzvuHAA1WFbegCXlP0Zxw2KUutr+f7ktAScTOyR05M9mJj6+TNRVpUs9+Swdw7FGVoSkm+/0j2UlDQFOliGbg278iq4WeGNCrr6q21TIFYTG9/V2YPqgCVGEaJ6E1sPDa1do7vSx/kLS02q10ilbf3lm4ia35iwrL8UbRy7Cebkv4IKCd/DmkXPw8u7BWLMLOFz1HsobGlATCqVUBhHvuMJCHF18FTaFroFVdODgof/DCG8VTvLtjQ2+DgdytMALqPXEvz755BZvv7P/EOspG566289mT9HZ9cA9/Swdw7GmuQEfHbFirMhybMg1r+aaP9aGRSihEORIRA248UE3Xlz3BYbczNLU6eOeWqtFXS9TgpSsKKgJhSAJArxa4Dzo9+P1775DeUMDDtbXY3edgJrQcijyLHwFBU9KEgLR1wG0ri2aALV+t6/bjcpg0Hj/qNxclHg8yHc64bPb4bFaIQiH8ONtRyOiWDFgwP/D/UPvADC0Qx5rV/wh1hM2PDX3sznM+XW3OtvR3XTm75iefpaO4bgtzJvImgq65qlooZCxqUxp7Wqu/q8kQTR/zJDb7TR1+rin1mpRenRWkIrIMqqDQdgkyQi8B/x+LPr2W1QGg/im1ouGcA0ikTJUBYOQFQWXHH00RuTn43+He2F/zQ7sqdra5O03tTpsEUUUOZ3o63bj6Lw8DM7NxdDc3GaHY8TrCf/HesIf0cl+NuNLy3RcUe44nfnz39PP0jEcA02u4hqfM4dc84puc7W55ilmetmC3h9XC7sMuj1fUzVZ39QPwzcNI3pkrVZXWHJkCiwSMMmX+AKdzatOrQ1SoWgUVcEg7JKEXLsdgBp4X922DZXBIKoCAWPwRE0oBAXATaNH49oR6kbSmlAIL2/b1uRxvPbdd8B337XqmAsdjoQJcQO8XhQ6neq+BbStA01PqYfsCQEfSPzZvKvkwYTnZEnZJCwpn9LtVsczUU/5+U+XrArH4aoqhMrKYgdHxHdeaKp0IdmKLoMuNaOpmiw9GJtPKaa7Vqu7begSBRmLy6ZClmWuOmkCkQgWHpyAQLgaDmsuIooVz+89GYfLnkSVFnT1wFundVwwB15/OIwF336b9LYFAKsPHMC2qiqjM0QqrKKI/h5PY/jVwnCJxwOX1dqux51MT6mH7EkBp7mQ353LRjJRT/n5T6eUwvGhQ4fw5ptvYuXKlfjuu+9w5MgR5Obm4oQTTsCNN96I448/vrOOs0PU79yJwN69sOTkJNboWq3q59ow8pcomaZqsoY4v435V5fOWq3utmmmtGAZRFHE4rLuvVmpOYqioD4SQWUgAJfVavTB3V9Xhxe++QZV2mS1Cu3fhkgEwGs4/ag1+MtIEcvKS/Hq3vH4bvsvk96+JAgIRCJQtOEY+/1+nFBUhJAsoy4cRmUggOpQSD0WAJvKy1s8ZslSBId9MKz2YRibH8Kk3ntQ4vWit9sNqQtfU3tCPWRPCjgthfzuXjaSaXrCz3+6pRSOn332WcyePRsDBgzAKaecgoKCAuzatQvvvPMO3nnnHTzwwAMoLS3trGNtP1mGIEmwahOLiDpTUyutmVirlSkbulIxpegtyLLcrVadFEVBrRY8PVYrCpxOAGrgfW7rVnWUsGmFN6SdxTIPnghEo3ijiZIFSbTgaMdXAEahtGAZAuGz8FzVXTg+9xC+5/sW0WgU/kgEVcEgDtXXY83Bg3j122+1YN06kiCgn7YKXOL1YqD27wCvF7/d9YQRcv4w9A4Afdr1/WqrTPw/lqqeEnBaCvnf1A/rEWUjmaQn/PynW0rh+LjjjsNzzz2Hk046Kebza9euxYwZM/CnP/0JEydOhM3UFoeIuofueIozE1adooqCmmAQlcEgcmw2FGqBd19dHZ796itUmkoaqgIBRLT9CTNHjcJ0U+BdumNH0tt3SBIiplKvXi4Xph9zTMyUtY0NF8Jr9+DiovdQFQphY1kZdtfWYn/NRuRGnVi39yD+920Zmu70myjHZksagPu43bCIicGsp9TGZoqeEnCaC/nxey/eqpwSczaIKF1SCsfnn39+0s+fdNJJGDduHD766CNs3boVxx57bIccHBF1rUwIm6norEAWkWWjTjfXbkcvlwuAGnjnffmlusKrlTRUB4PQo6s58AajUby1a1fS23dbrY0j1KEG3htGjjR67+abevA6LbEv0x6rFT845hhjGMam8nLsq30cu2trMae2Fn7TBLeWiAD6eDwo0euBTRvj8rSNeq3R3MbTu0oeTHr9TKtjp87R1HOsD0QyB2fz2SCAAZnSp8M25Fm0F3CLJav2+BH1KN1p9S9+Z3tLm5VC0aixiptnt6PY7QYA7K2rw1NbtsQE3hqt1hYAZo4ciekjRxq3sWL37qTHkxN3xqy3y4UbR42KDbwOB/Ls9oRWZB6rFddr92FWHQziW9MmOH1U8n6/v9mJb/FcFktsN4icHJR4POjn8cDWyrZoTWlp4+mDe+6KCciZWsdOXaunlI1Q6ymKAiiK2vggw3VIkt2/fz8+/vhjFBUVYdiwYR1xk0TUxbrTznj12Kbg/LxXMMb+OraUBzHW8QpQoJaFVNYfwjd7H4kpaTCvqM4YORIztDAakWW8t2dPwn2IAHLtdqOdGKAG3luOPTampEEPvPGlBm6rFddpq8jNicgyDvr9RvA1v5lDemv0drliSiH2yeej0N0bV/RZlbDJeFl5KbZUtn/1tqmQc1fJg3hwz10ck05J9ZSykWylB934trZNdv7S5zmIIiDLEG02iBm8mNruIwuHw/jFL36BUCiEu+++G1IzqxC5ubnqQIs0sdntECWJq9tZgM9xavRV2KlFSzClaDkAC6b2Xm50hBBFEVOK3ur041AUBf5wWO3AEAig0OVCP48HALCnthaPbdyIykAAe/0r4Q/fii+jQeNrZ44ejZmj1WMuqwM+2Lcv4fYlQUC+wwG7xWL8jHwRvBRnDynA6YU71MCrveXYbJDiXq9yLBb8YNSoNj222lBIDb01NdhdU4Nd2vt76+piaopb4pAktf43JwcDtTKIgTk5KPF64Yj7uV9SdgwWl01BTlV+zPNnfr7b+3/lkmL9dhNv5+6jHsGSsklYXNZYx27+GUsF/093vMWHSyEKctL/20vKJkFWREzt1bVBlc9z1zMCrb6qmyTwJlvtFbQZDoI2lVewWiFYLJBsNjX82u1GCBasVuNfORRCtL4ehQMGwJGhDRLa9VMoyzJ+85vf4LPPPsOVV16JSy65pNnrV1dXt+fu2sXn8yEUDEKORlNuJk/dS1sGBmS7SBSYUrAYk3zLYP7WTfItgSzLiETFNn9PFW2ksL6KW+Ryob8WePfW1uLRL76IKWkIm16Erz/mGNyghdFQOIwPkwRemyjC53BAAhCJRDDJtwQN3ghcxx9vlDRsDpyPj+quwtReKzG58E31MUciWFZeircqp2JKiQ3nxK1WKbKcUmgF1PHJh+rrY1Z/9XKIikAgpdsqdDiMVWBzOUSRaThGvPjnSH/+zD2h9VX3Yc6vMcm3BPFPa0fXA0/yLcGyIxcY5TrJ7rMlHfV/urv18+50SgSLjzTVL1wtWerK11K+dqfOWMHVg238v/GfU5TGs0imybwwBV0IAgRJgqCFXMFmU+c6WK1qCLZYGt/iP25mAVTR3qKKAtFqRVV1NexpaODga0Ugb3M4VhQF99xzDxYvXoypU6fiT3/6U1tviojSLNVTnFFFQbUWdiuDQfR2uVDi9QJQA+9DGzcaYbgyGETUVB9rDrwygE8OHEi4fafFAp/dHrMZrZfLhbvGjjVKGorcbuRYLHBZLAklA06LBZcNHWp8PBYbUVDeF0vKL4YgCO0+xV8fiWBvkgC8p7bWaL/WGubhGOYQXOL1wt1BwzHSPbo3k+rYu1s/787WHVs49hQxZQnNBNz49w16mYL+viiqr4Omf0UtsBrB1maLDbSSFPu+OfC2cy9Cd9emcCzLMn77299i4cKFmDJlCu6///60lksQdZRsXlmKyHJjoA0EUOx2Y2BODgC1pOHBDRuMy80dGgBg+jHHYKYWeBUAnx46lHD7Hqs1oftCL6cTd59wgrHCq/8bXx4AqIH3ksGDjY9TXWVKtVWdoig4EgioZRBxQfhwQ0Or7xcAfHa7EXr1euABXTgcozWjezsjFGVaHTvDYKLObuGYEPzMp+mjUfVyLfxFJQlyNNr4xfr/DUFoHM6lv6+tcOrXSTq4K9nntNXThLDZ1NfE3a/xWMyPy/QY4j8vmG83PtyaH5ceavVga7VC0CfxmkIuJEld4dWDbfybxaJeR7setU3K4dgcjEtLS/GPf/yj2Tpjou6kp60sBaNRY/W2MhBAX48Hg0yB94H1643L4zd//WDECMwaPRqAOj543eHDMZcLUDs0+BwOeEyrnL1cLvzypJNiwm6e3Z60K4LDYsGUo4/u2AfdjGSt6oLRKPZpbdHiQ3BbhmOUeL0Y4PHEtEXzprn3ezpG96Y64a25P0yXlE1SS3864A/T7tjPu7O1t4WjoihQwmHI4TCUSMQIigY9/GkTaQUt/IkejxECBYsFNocDoVAoIYAaQToahRKJQI5EoESjjfejKMYpe9NBxf6rHwfQGKzjw2OywKwoamcY/YxQfFAXRYh6WI1fjdXKDARJMibwGqULpgCb8LE2qZfSJ6VwbA7GkyZNwj//+U8GY+pRmltZGurc2uTXdeWqsj5SuEqr0e3n8eDo3FwAauD9x9q1Rhj2x4W760aMwI164BUEbCwri7lcFATk2e3w2e3IMfW5LXK58JuTT1aDrtalITdJhwYAsEsSLhw0qIMfdfsoioLKYBAv7x2FsiPPIxzcikDwO5R+/SXqgweAFMZjeK3WmHZoegju28RwjHRL1+jeVFt1Nf+H6ZQO/cO0u/Xz7myplL7EBOFwWA2NgqCubNpskHJzIblcxmas5k7dx3M6nWho7VkZRVEDsh6i4y6LWcXVaaFWkCQ1jJpXpptaUdbCuVHaoNfjCoKxiks9T0rh+NFHH8XChQvhcrkwaNAgPP744wnXmThxIo5pRfuiniCbT8H3ZE2tLOmfM18HaP+qsqIoqAuHUalNUKsIBlHi8WBwXh4AYHdtLe7/7DMj8AbMpx2hBl49HIuCgE3l5TGXWwRBXcHVWo7pipxO/O573zM+r3doSLbZyy5JOH/gwDY9vq4UlmVjOEb8KnBdOAygdf8fBQiw2AaixJuDk/IbYjbE5dpsyU/hZqB0ju5NtY69uT9MpxYtwSRfxwXYTKqDbouO/N1j/hm5MH8p3jxyIZaUXwIlEsGknNeNFVo9iAIw6lct+fmw5ORAcrnUN4cjcTW2s2iBHAAWbjoBoqBg2ugNCVdbtHksZEXAZceub/n2mvh/3T3+t1NHSikc79N2itfX1+M///lP0uv069cva8JxqqfgGaa7j+ZWllpTryhrHRqqTH12B3g8GKrtkt1dW4u/ffqpUdIQjtvEde3w4UY4tggCvqyoiLncLklq2YIWanWFTif+OH68UcqQr5U8JHvRt0sSzh0woH3fqDSpCYWwr6oKOyorY4Zj7EtxOIZNckC0HQO7fSiO84UxsfcB7JIn4+P6mZha9HanBqaueD1IZXRvuuuBzfcb/4fplKLlKXe4aEqm1UG3RXvLv/Qa2WVHLsTS6qkodb2E84QFiFQC51lfhOwJY2n1FYCi4ML8pZCcTogOR2MIdjohOZ1dF4RbIAoKXt10EgDEBORFm8fi1U0n4fJj16br0KibSikc33///bj//vs761i6nVQ3d/S0etaeLNnK0gX5SzHOvRCH6/bgxZ2j8ML2M2GxDcAVJepzvbu2Fn9es8YoeYjGhbRrhg83wrFVFLG1sjLmcpfFYtToFjqdxucLnU78ZcIEtdxBK2lwJunQAKiB96z+/TvhO9J6HRX6IrKMg/X1xoa4PXV1xvvVKQ7H8NoLUOAqxokFwZjOEAUOB96smIyt9cOxrWE4FjSEtV68nV+D2hWvB6mM7m2uHrgrJf/DtGN636ZaB52pWvu7R1EUKJFI45tepwsAoghZBqb4XsNFgz6F5BqulkLY7bjaug/ObashCwPgO35CWh5jKvRAbA7I5mCcbEWZqDnstt1OqWzu4E7pzBOWZWN1V1/h3a9ciHVh9TkZbXsJP/1oMx7YEsQ/ouVQa1MbA0dR0Y9QOuYgADXwfltVFXP7Xq1Dg89uR2+Xy/h8odOJe085pTHwOhwJI4V1NknC6f36dcjj7YrVylRDX104jD1x45F319Zib20tIimsAtv14Rheb2MtsMeD/l5vTIeMeKUFy1BasAw/3vZwl9agpvP1IJNH9yb7w3Rq7+UdctuZ/LhTlex3z+TchTjftgDhykhsfazFoq74ejywuFwQHQ6IDgeucR2AaLMBGJFw+5eO2ZT0fhd0RAlDJzAH5Ne2jEVElhiMqc0YjjtAKps7uFO68wWjUZT5/TGjg4/OycHIggIAaknDPR9/jMpAALWmkcK6gqIJmDVafU4O+kUc8ZsHTwhwWT2ISv1htRTAYhuEZeUnoLRgGQqdTvz91FORZ2pLZm3itKNVFHFK376d8fCb1RWrlclC39Ijk7Do4BiMtd2L+op38X+7GsNweRuHYwzIzUWJ222sBPdyuZocjtGSdNWgpuv1IFNH9zZV8iCKIib52l9ylqmPO1X6prjzHa/gTag/NxLCmOR9DaLTA6tWByw6HJC0ICw08wdiKjK5hGHa6A1GMLaIUQZjajOG4w4Q/4v1X3t+guGurc2uzunX5U7p1tE7NJgnqQ3OzcXowkIAwK6aGvxGC7z1SYoTrx42zAjHdknC7tpa4zJREIwa3ahYgmH51cZzUuB04v+dfjry7Hasr5+MPZETsD0wyvTLOz8mBI7r06ezvxUxUl0J7uzVygZtOIbd/x/k1byG/+wS8VBwG4LBpVCUBnzbytuxiiL6acMxzIMxBpiGY3TUNK1016Cyc4KquZIH84S/bKTIMuRQCEoopLZKg7op7u2GyxGFFRYhgohixfs5t+PS47/o1GPJ5BKGRZsbg3FElrBo81gGZGoThuN2auoX67aG4QCSr84Nc37drXdKdwRzhwZz4B2Sl4fjTIH3lx99hKpgMKFDAwBcNWyYEY6dFgv21dUZl1lFET67HYLUG25bDkq8jX14CxwO/N8ZZ2Bz4Dw4LHm4vM/7cSuO9TG3c1Lv3gCAb6K52F43KqPqFduyEtze1UpFUVAeCCRMh9tdW4tD9fUt34BJnjYcI35CXHEXDcfIhBrU7t45oaM0V/IgiiIi0e5T8tBeehiWg0Eo0ajafsxmg+T1wpqXB4vXiyX7zsHSA6cYgVQNqOMgSFKnB8JMLGGID+j6x+bjJWothuN2aOkXa7LVOX1sa3feKd0UvUODeehERTCIYXl5OL6oCIAaeO/+8ENUJenQAABXDh1qhGOnxYKDprDlkKSYSWr6MAsAyHc48O8zzzTGCju0tjz691fIWQxA/f5aRBEHpRlYHVCfu9aeis/EesW2rgS3ZrXSPBxjT1xbtGSr802TYLMfhQFeD07Orzf6Apd4vchJ83CMdD+n6V61ziTNlTxMKXqrQ84SZColGlXDcChkhGHRZoM1Lw/W/HxYPB5YPB6IWmeaRZvHYuHW2JXaZCu6nSmTShiSrVx39feDehaG43Zo6Rfr1vrhMatz8cHYfN1M/YUYkWVU64HXtMI73OfD2F69AKiB96crV6IyGEzaRuvKoUONcOyyWlFmavLuNnVo8DkcRr9eQA28j5x1ltGj19VMzZxFFI37MJ9u78gygkytV2zLSrC+WikhhEC4Gk9sH4x+woqYDXEH/X4k/vnSNI8+HMPrRYN0Mr6LTsX5vffg6v7rsKJyCpaUT0VJwWJcmEE/4+l8Ttuyas12kN2f3kFCL5OAoqhT1mw22PLzYc3LUzfOeb0QTX3JzWRFSLpSq38sK51/1iWTShgy4ftBPQvDcTu09Is1fgf8EOe3GOb6Ju0rj2FZjlnd1QPvCJ8PJ2olBLtqanDnBx+gOhhMOjvsyqFDjXDsslpjNlXl2Gwxo4OHaP16AcBnt+Pxc84xLm+qQwOgBl69bKI9smETZEsrwRFZxr66Ouypq8OKg32xsXIF3NG/obZhN2rDYXzTyvsRARRrm+DiyyHy7PaY1frvFyxGacEGAGLG/xGYDm1ZtWY7yO7HmCgXCqkT5RRFnSZnt8NaWKgO0dBWhlu7aa65bhBdEVAzrYQh3d8P6nkYjjtRfC1hUys+QPvDQjAaRYVpdVcvaRiZn2/UzO6qqcGP/ve/pB0aAODyIUOMcOy2WlEVDAJQA1GuKez6HA4M0/r1AuoK75PnnmtMWmuqQwOgBt5j8vPb9VjboqdvetJ/1hA9jJrALvx9sxd58irs1soi9tfVJfRdrm7m9hySZJQ/mN/6eTzN/kEDpL9UobN11OptW1atO3tDJVemW2aMGJZl431jtLA2ZliRZUDfJ6GPVnY4YC0uhsXrhcXrheR2d8vRwyxhoGzAcNxJ2ltLqCgKGiIRVJhWdysDAVQEAhhZUIBxxcUA1MB763vvNVkDetmQIUY49thsRjCWtA4N5sBrDq0+hwNzJ06Ez+FArt3e7OYoSRBiwnIm6kmbnqKKgoN+v1H+sKosD9/WPAmE7kR9WO3CsbOVt1XkdGKgtvpbK46Hz9UPV/bfgkKHo80jkjO1/KSjpHv1tjPPhKT7sWWaJUcmQ5AjuMC1wFj1BQCIIt72XwoZEkpzF6n/V0RRDcE2GyS7XW2j5nRC1KbJSU4n0E3GjjeHJQyUDRiOO0FTtYSKouD1Q2ei3H8AxzqXx5Q0jC4owHitDdiumhrc/O67CCbp0ACogVcPxx6bzQjGVlFEvins+ux2jNLalwFqScO888+Hz26H12ZrdiOaJAjG+OLurrtuevJrwzF2x73tq6tLupmxKTZRjOkEob8lDscIAvgOgLOJWyIgM4b5dNaZkEx4bOmUUA8cqMfS+qsAABcNXAmL2w3R4cAbu8/EssOn49LhH8M3cpwajCVJXQnuAQG4OSxhoGzAcNxOeocGc0nDp+Ur4A2/gjxPNQB10MOumho8uPImhGUZW5PczmVDhhjh2GuzGcHYIUmxgdfhwLGmOlyf3Y5nL7gAPocD7iZGCutEQYjp8JANMqFVV3NkRUFZQwN219So45Fra40RyUdSHI6Rrw/H0N4OKufA5+yL7/df3ebhGJRcuuvYO/NMSLofW1dqth64qAiX5X4Nx4FVWPjNNDhLSjBtoFpfu+hbvaxgCwBHuh8GEXUwhuMkIrKM6mAwaUnDcUVFOK1vY+C9YcWKJB0aPgUA9LMNMaag5dhsxmqf22pFflxJw3GmwJtnt+P5SZPgcziaHHtrrg0s8XpjLmNtYKNMqX8NRCLYq4dfU0u0PbW1SXs4N8UiCOjn8WCgqR2a/q/Hao279h7tjcG4M6Srjr0rzoT0xBp9RVGgRKNQwmH1zTRMQ3Q4YO3dG5acnIR64Mv6fgnRbs+onr5E1LmyJhwHg0Ec0nbr+w8ciClpGFNUhNP79QOgBt4Zy5cn7dAAqJ0e9HCca7cbwTjHZksoaRijtRbTr/tSaSny7PYWNzSJgoC+Hk8L12FtYGt0Zf2roiioMA3H2N2O4Ri5NhtKvF4MzMlBiT4pLicHxS4XLN1wE09PlI469q46E9Jda/QVfVNcNAolEjH+haJAASBIEkSrFZbc3MaWaW43JJer2XKITOrpS0SdLyvC8TfffIPx48c3eXlUUYxwnGu3Q0Fjh4b4wHu8KfDm2Gx4dfJk5NntLQYWURDQ2+XqiIcDgLWB6RQyDceIH5CRynAMURDQz+1OqAcu8XqR20R/02zSUucECBaU5qfnj8B01bG39kyIYuqcEPNvXJcF483k7frLsKx+KkpdL+EC90K87b8US8qvgtzQgAtcC9QQqQdJ7d+Eci7zx6brCvGfN3V60I8x/ngAQLZa1YUI/b61rzU/NoMkqfW/kgTJ7YbkdsPicqkb5FwuSC5Xq1um6TKppy8Rdb6sCMeFWsmCRRSRZ7Eg3+Uy2o7l2+0xNby5NhsWTZmCHK1DQ3O/oN+qmKz+snKmp3whWW3gUGeyimYVyy1aT1EUVIdCav1vXZ1RB9yW4Rhuq9XoCGEOwX09npi2d0uOTMFuQcZoO9toAS2fHZlalJ7vRTrr2KcULtHKA7SWYdEoEI1CiUZxnvgcoCgIV2hX1jeIiSIEvZOCJEGwWCBYrUaAFCwW4/0le8/GsiPn4JJB/8PUo76BIo/EZfKXsO56F6/vvgpWnw+lvZer96kHU1PIVvRgq78f1/ZM0UOsqeuDqB2LaLMZbxBF4zpKNApJURDy+yFrdcGKLKtT5Ox2CHY7RLtd7RBht6u3YbdDsNk6pFVaZ/f0XbDpBIiCkvS2Fm0eC1kRmt0ER0QdLyvCsc/nQ3l5Ob7+zW9Q+/nncPTv3+R1BUGAz9G4wSLTyxfiawOHu7Zm3PGm2ju1K3utRmQZ+/3+2K4Q2ua4mlCo1bcjQB2OUZKkHtinDcdoSab/rHW1ls6OTClajnRMFO6oOvaYEgDzCm9c39wE2sqpOdxKHo+6KupwQLDZIFqtEG02Nfjqby2UcwGAWJ2rhcBvARQbn7+y/3ew5uZCVgrgGT68VY+vmQfeWOZgXoVuhtPpRINpsmZX6YqevqKgJL0t830TUdfKinAsCAJ8Pl+b+rZmevlCfG0gAEwpWJxRx5tq6OuMkFgbCiXUAe/R2qLFD8dojkOSjOA7UKsDbu1wjJZk+s9aOjTfOSE9L19N/WGmyDIm5bwOyDKiDY2n+5fVXAoRUbUkIb6EoeFyyIKEybmvqauodru6kqqt7hrvm1d4tX9Fm029jsXSYe3DuqRNlx7uO+bWOlVX9PRNFraThXKi7k7fAxBtaECm75zJinDcXpna2qipuscpBYuNgJwJx5tq6GtrSIwqCg75/dhXX48dVVUxq8GV2rS/1ipyOmNWf/W3IqezzcMxWiNTf9bSKVM6JyiKYpQwyJGIutFL6zSir4Lqq7kQRYhawLWGbXjjyEWweL2YUvK+GnitVizZcxaWHTkTl474BHmjJ0DUvo66XlOlDZcdux6LNo/Fgk0nJPzh0JGh1RyQ2RGDuhNFltV2iFoHGCUcVl8fta4wMQTBeP2z9e4NKYP31jAct1Km/ILWtVT3OKVgsbGanAnHm2roa+769eFw0s1we9s4HKPE640ph+jv9cKV4oadjpRpP2vp1tWdE4yWX1oAViKRxvIGSYJosUC0WCDl5EDSNnrptbJ6SYNgtRr1rlfjIOyb1+LVTRfCVlSEaUO0Xrnf6SuDmwHEt+GjrpQJpQ3siEGZolWBV98UKwjGGSzBalV7hBcUwJqTA0tOjlrypU+JdLnUqZEuFwr79UNNGkqlWovhuJUyrbVRS3WPW+uHZ9Tx6sfW2tCnKApOcr6KV+pcaAjsRDi4Fe8cXIqnamtxJMX/UPkOh9oOLScHA/R/vV70crmaHYudLpn2s5ZOzXWFmNp7eatuQ98YpkSjRl1vfBcH/UXeeLHXVoBFux2WgoKYF3h901cqpQxcGcxsHVna0NYNduyIQZ1F39/QVNjVe34nBF6trEu022HNz1dbIObkqF1g9KBrCr2S0wnR4WjVRljJ4QAYjru3TBw/3NKGtG0NwxOO95v6Ybir5MGE63ZVJ4Rkoe/cvDeMYRjx9cDqcIzG7295M7etD8cY4PViYG4u+rvdRlmE12br1MfVkTLtZ60rN0cmu/3mzo6IoogL8t6IDb5a2YO+yc2Ir1rHBr2Dg2ixqKu8pjfBYmms49UGQ4gd+LPT2pVBdi9Ij476A6Ytq9Cd3RGDeh591LkebmXT+0o4rL4m6mFXUdSzXqb9DJLDAUtRESweDyy5uWrgNa3wivr7KQTenoThuAWZPn44XlPH+039MHzTMAIP7rkrJiB3RScERVHwyoFTsfRgPoZZfoIc+ROsr3DgX1/V4B/hPUCTI1cSOa0eDM6xx9QBD/B6Uex2G72mLRYLIuloY9BOmfiz1hUdNJoK4LIiYpjza8iKYJQ5yJEIzrO8ANnVgHC9hIhSGbPSC0lqfIF3OIxVXkEPv6YNbl2ttSuDmXCKP1t1RGlDqqvQXdERg7qHhHIG8yqvNtRGMLU5FCRJLeHSyhokrxcW/U0r+zLCrsMRE3zFVnZRylYMxy3IlPHDrdXU8d5V8iAe3HMXvmkYYZym7+hOCKFoFPv9/ph2aLtrarC9JoBQdAEAYFcrbkcQRFitg1DizcFJBfVGZ4it4Wl4r/ZalPbQDWqZ+LPWFR00zAH8wvylxi8EhBrwTcMIDBE+R6S21gi3Um4uLilZB4fXi4hwXOxqr9WakZvaUlkZZPeC9Omo0oZUVqG7oiMGpUezq7v6fgazuPpdwWKBNTcXkter1vB6vQkhV3I4jNIG0cq9Cx1FUJQU+li1U2VlZVfdVQKfz4dPbr0VNRs3NtvnuKfTg41e2tCWgFMVDCbdEHfA7zfGabeG22pFjrMEPmcfnFpUbYTgjYErYZXENp/K764rx5msI35uAFP9r2m0rxKN4u26aVhWfxVKXS9hUs7reLv+MiytuQxT+y3HxUM+MXr4ina7Ueubrt63qWoq2LYUePXL9aCWzcG4K57rpv6Aac/3/fqXZhph+5mrnurgI+55Mv3/tLFZ11y7G/dxPKMto9ZvXHQ4Gld3vd7Y2l39X22ao2i3p+UsV1fw+Xxpy4Q+n6/F63DlOMu0dlNcRJZxQFsFjq8HTnU4Rm+Xq7EEIifH2ByXH3Nap4/xNQNz3mr2+JNJZ21sNmjtz43R7kxOnOBmnopmDK/QxvlOO2ojbAeL8Nquq7A8cBkiskULJbsA9O26B9oJ2royyO4FXaczShu4wa77UBSlsZwhFIIcCqkfh0KNr1ta/a5gnjJpscTW7ppKGURTva5kCr5c3e0eGI6zTPymuIUHz8Jw64KYAKwPx4ikOBzD3BNYf7+/xwNHF7RFM5+aN3cxyNbpcu1lTG/Tujm8WXWR+nMD9edmyf5zcYF7odHn1yAIjeOK9bZnpultol4HrL2ZV0WuOHo7luw5ExHZ0qPCYFsHazBcdZ2OLm3gBrvMo5c4yA0NiAYCkBsaIIfDxgKNsSHXZoPF44HV54PV51NXd7WQqwddo5xBez1j7W7Pw3CcBfThGAv3j8CHZftQLFwGhLZgV00ID4VqUrqtQm04hhGCtf7AhU4nxDS+QMR3MZjkW5L10+Va0mw/X8BY4X2rbhqW1V6KyTkLMCnvDbxdczGWVF0ByenERQPeb+ztGzfVTf+3tS3PGAYbMVx1rY6cDMgNdp3H/Ed7QocavT2jeSy7/rqmb2DTyxrcbtiOPhr2oiJYcnJg8XggeTzGvwy8xHDcg9RHIk22RVOHY6jlCodauB2rNhxDD79GKYTXC1cGnxLSA/DisqlYduSCHj9dLqF+V5aNkgajfU8LjFHEdjss+fmQ3G6jhZlgsWDxd6di2YFTcNnINZg2ugyCeAq+LxyBY/NavLppCuzFxZg2vP2/6BkGGzFcdW/cYNc65s1qst5vVxQR8PvV2t24cgaD6cyUUaKltWiExQJRP2PldKqB1+2GNS8Plrw8WHNz1fdzc7OuNRmlhuG4m1EUBWUNDUlrgctS3Mjgs6st0WAbBZ+zLy4s3o0Srxe93e5mh2Nkcn1vpk2Xi1nFaKoGNxXJflHoAyusVohut7rqYbU2rnwIgvqLQBDU8Z3axhB9mpEx1CIZq137Rf8FgMYSiI78Rc8wGIvhqnvryFXodIh5zdJfq8zDc/TLk/0BHv/6ZPo6/bUv5urms01WKxwFBZD69oU1NxcWjyd2+qT+uqVvbDN1qTGfsWLopY6QdeH4rdA1sJV7MjLYmQWjUexN0hFitzEco3UkQUB/jydpPXDscIwwzJvimtNRvW87I2SnY9QwZDmh+4KiKLEDKMwBVpu2ZvTglSSjVjfmtky/iOJrefUVX316kf7Lo6N1xS96hsFY3T1cUeZSZFndbBYKQdY2nCmhUGxLMW1gRMyKrPav8b7VarxuGWFUUdTXLEFQ/zDX+o+LdjsEmw2Sy2XU70pOpzp0Qp+0pm1iyy8sTGtXKyJd1oXjrhhq0FqKoqAiGGwMv3pv4NpaHPT7UxiNAeTYbLG1wNq/fUzDMTpKR/W+bctz0Vyg1vs4Ty1aElNzHH/7bWEOwXqvSr0+982GKyGKQKlvCSRtt7K+UWPJnrMgixZcNmptpwXY7o5hkKj9YsoUTN0W5FAoZi+BeTKkvXdv2Hw+WHw+WLSSKuMPd7s9dlVWC8RcnaVskHW/qc+3vghLTk6nDjWIF5Zl7NdCb/ybP0lfxKaIAPpotb/mADzA60We3d7hx90cc0DWyxhS/f61JWQ3Faj1YDzM+TWmFL2FSES7XFGwpPxiQJYxyRe7Ci0ARqkBgNjNHKaV4MY7F43TeRafD5K2AuzaW4yF206Da+BATDt2o3H1RZvHYtF3armA5HK1+vtCRK2TTaO2Y1Z9g8HkwddUpiDa7bAVFcGanw9bfn7j1DRt45nF4+Ef60RNyMr/GR0R7JKpbmI4xv4Uh2O4LJbY8cg5ORjg9aKv2w1bBjUE74j63lSfC/P1lWgUkzyL8GbVRfimYQSGWjfhdvdfECqXENVKT86TnofsDiISEiHX18fcVkLNnH46UJIgSpIaft3uxjHEDkfCIAoAuKz4K4gOB17ddDIgCJxoRtRFuvuo7YT6XtPoYH3117wxTV/xFe122Hv3hjU/X203pr9WmcsUXC6u8BK1UVaGY6DtwS4iyzioj0iO6whRncJwDCBuOIZpNbjA4egWbWQ6qr63ueciod1YOIzzhP9CdjVgadVVeLtqCiKwYmqft3DRwJUQpOGwO50IR6PGbuYrxZ3qLwnxpNi2YuZevlrtnKCvDscF4JakMi6WiDpGJo3aVqLRxhVdbZhEwohg/TVF/8Nc30ug1/Rqq76WvDxY8/LU4BvXaszi9UJyu3vs5DSiTJC14bilYFcbCqlt0erqsLumRg3AdXXYW1ub8nCM/nEBuCuHY3SW+PKHttb3KoqCN49cGDtgYt85ON/5qrGhzZim5nBA0iYRXeHegeXvRBGRrbCIUVx11h4ARwFI3whSTjTrObLpdH1315V/mCqyDDkQUN+CQcjBoNqFAVBXdrXNsZLDAWvv3mqQzclR63jja3e1P96Nbgw2m7pRzeXiFDWiNOu+6awd9CA3Of81nOBcgAX7RuCZrwvwtnAEQngLdtfWoiIQSOk2Cx0OlHi9GKiVQOj9gYvSPByjMxjBOP91XOhbCiWqYFLO61CiUSwpnwYlHMYF3tcaV2X1jgtJvF1/GZbVX4JSzyu4MO8NvF03DUuqroQlLw8XH72qcWOI1tJHl4kDIzLxmKhtuvvp+mzTkX+YGmerwmHIgQCigQCUQEB9LQOMSWm2wkLYiopgKyyEJTdXXeHVV3lZ0kDUrWVFOG5oaMDOnTuxfNs2vLUrF1/Wvw575Pf49+b9CMkygDcBtG44Rj+PBwPjNsSVeL1wd9O/9I1BEvp0oSb+NYvUB1HqegnnSQsRqYZ6WlAQcIFrARCNQobUuMs5bmqavtNZkCQs3nUGlh05C5cO/QiXjNwP0Toe37fqAybOhy0/v8mVu0wbGJGJx0Rtl0mn66llLf1hqihKTPcGRRs6IUciiSPQoZ2t0ja12YuK4OjXD7bCQrXGNz8f1rw8SA5HVz5EIupCPT4cf/XVV7j00ktx6FBL0beRz26P6QShv7U0HCOdFHNjdnO4jfs46eAJvX+l/q8gQHI41F8O+ik/fSSwxYKrpG+0657Q2OdSO014tXRIC8ATWjxm8YhXCxpfAWjs5tBcf9vWDIy45uSvU/32tQuHWPRMrCPvHsz//y4ZuQ4Lvzger24aj0htLSYXrzD+uDe/numrvJK20quXQ4jm0gaXC9acHIhOZ7fYA0JEHafHh+P169cnDcaSIKBf3HAM/c3b1LSwTqToodVUipA04DZTohATcrWNHmLcJCFj0pDer1J/M30sWiwpbUZrq7b0t83EgRGZeEzUMVhHnlmUSARyMIhoMAglFMLr20/B67tPwsX9luMC53to2AFMLtgHZXAIi7afDXvv3rhmcrm6uS0vD5LXq/bz7eLWl0TUvQiKksLusnZKx+SbQCCAv//976ipqYHzyy9RVFmJwUcdhb4dPBwjfuXWCLdJ/oUsQ4Gpz656A0bP3fiAa0xCs1rVBu56iYJ5Ulrc1DTj/Syse0vXhjzqWl3xPOurkvrpeq4cdz5FltXNbtrGt2gwCKsoIhwOq3/w2+3q5lyPB699dzqsTju+f/4ho5uD5PHA6vPh2VedkGVg1g3Z9xrYXfl8Pk7IyxLpfK59Pl+L1+nx4Vjn8/nwya23ombjRjj6949ZqYWixNbetvB+UuZgq4fa+HAbX39rDrVaCzFBkhpHd2ZxwG0PhuPs0NnPc1N15AzIHUNvfRbVOj/EbHrTNuFacnJg79UL+UcdhaAkqRvfcnPVLhCs+e1xGI6zR6aH4x5fVhFDEKBEowhXVBgfx4dafSY8RNEIsaIeUuNDbfzs+Sbe2lqiwHZSROnBOvLWUxQF0IdY6OPVTRMm9QEXCRvfBMEYs24vKoK9Tx/Ye/UyNrxZ8/KMel+GJiLqSlkVjp0DBiB0+DAc/fsbPSaN5uumvpNG4E3zJgy2kyJKj2yvI1cURQ222kALfahF/LhiQ/wZMosFktsNUdvcZkxus9kaJ7i53epIY3Z+IKIMk1Xh2FZQAGtBAezFxek+lFZhOymi9GjLZtFMEhNu9fZl+oqueWKbmXn/A6CeJdM28UoOB6zFxbD6fLDm5jb2H9dGGQumTg96H2CxGw85IqLsxlevDMd2UkTZy9joax6hHleuYLwvy41lYYoSE24tXm/jgAqvF5LNFrM3wpjWpo1O1wOu5Har3R3YzoyIsgjDcTfAdlJELTMGPWhjfeVwuHGl1FwKoIXHmPfNn2tKS9cx71sw9QyP/1e/DaNW1xR+IcuJ5VymkgV9z4Not6slC06n0blBb1FmlDK4XEb3BtFuZ7glImolhuNugGOJiVSKLKslAqEQAjU1CNTUqHWwplIA0W6H5HTC6vOpXQ3cblhcrphwaWzGBRo70mgbxoyBOeauM3Hh1mjPqK3eyqaJa4oeyvWJbJEIoF+mD6TQVmuNMKut0koul1qqoI1LN97Xyxi0NmaCzcawS0TUSRiOMxzHElO2MFZQtXApa+FS0epldXqdq5iXB2d+PuxFRbDm5xtTz6xaqy8hw2peFUVhoCUi6gYy67cHxWA7KepJFEVRhzo0NEBuaGjsfGAqNTDqZLV/7UVFsBUUwKJtBDMCcE4OCvv3R1VNTZofVesxGBMRdQ8MxxmsK9pJZWsv5Wx93F1BiUSMDglyMAi5ocEoWRDtdkguF5wlJbAWFKilD253TOmApNXMik5nsx0PBEnqqodERERZhOE4g3VFO6ls7aXc0x93Z4R/JRpVyxz0vrd6XW04HLvhTRSN0geL1wvH8OGw9+4Na36+0U6RfW2JiChTMRxnuWztpdzTH3dbw7/eH1df8Y0GAlBCIfVCQYBos6k9bS0Wo8RBysmBxeuF1etVuyR4PGrrMK+XLcCIiKjbYTimrO2l3BMed0L/W63TwuQ+7yBaX49XN52BqN+PiwZ9iMU7TsNrO07CJQPfwyTve6jfITeu+Jo6N5g7Pjj69YO9uBi2/HxYfD41DOtlD1Zr+h44ERFRJ2E4JgDZ20s5Ux+3orcJ01uEmcb3xkw4E4TGDWzaIAe97djFw9YAoohF287EGztPRUS24PJj1+KyE/ZAch6nDnlwOhsnnekfO53GprdM6/hARETU2fibjwBkby/lrn7cxlhfvU2ZHny1Gl7TFQGLxejaINpssBYWquN7tRVcY8CDwwFJ29AmSJIakiUJgiDgp6KIJecrCIctsFqBux7+HoDvddrjIyIi6u4Yjilreyl31uNWIhFEA4HGSW3BYMyGNaNdmdUK0W6HrbAQltxcWHNzjUEQRumC+f02lDHMm68gHAasViAcVj+eMZ01wERERE1hOM5yHdlLuTu1R2vL41ZkOWmnBv19o1+vKBorufbiYtiKitSaXY9HDb/6mxZ8BVHslMc4b76COU8puHGmgBnTBeNjAAzIRERETWA4znId2Uu5O7VHi3/ciixDDgYxpeR9RP1+hKoV1O/YETukQhDUzWo2m7FpzVpQAGtOjrpZzeOBxe1WV4Hz8mDJzU3bprX4YAw0BmIGZCIioqYxHGe5juylnGnt0RRFAfSRxFpHB72+tzTvdSjhMOq3K0anBr037yXHrIU1Lw/W/JPVUgdzeYPb3Vjm4HBkbJuyaDQ2GOv0j6NRBUBmHjsREVE6MRxTh+rs9mj6Cq8cDKob2kKhhCEUEZsNIb03ryiqm9QsFnW112JRV3lzc9VSB61Hr7k3r+RydVqpQ1eZdUPTx68GZAZjIiKiZBiOqcO1pz2aEo0awdcIwOGwWtag0ccMW1wuWPv2hcXngzUnRx1BbLUip6AA/kCgMRDro4ltNvbnJSIiomYxHFOHa6o9mnn6mr7imxB+BaEx/Ho8sPp8sBUUqMMnPB61rjc3V13hdbuTljX4fD6IlZVd/KiJiIioJ2A4pnYzevdGInjtq5OwcOtJmDbkQ1w04AMs3n4KXt10DsIVFZjc912I2kY2wWYzNrIZ5Q0ej1HmYMnJ4ehhIiIi6nIMx9QsRZYba3v1CW3mgRVaJwfBYsGSfefgtV2nYNrRH+Diwash2j246qw9sH/zNV765Hx4jzsO068MGjW+ot3O8EtEREQZheE4A6SrP7CiKI2T2sxlDvpmNkAtc7DZINhsEG022PPz1ZXevDxYTL16RacTOW8U4IZTArj+2pMhWk+BYLNBEATcAcA7X0E0WgzXUd17oxsRERH1bAzHGaCz+gMr0Wjjaq9p5Td+Wpsefq05ObDm58NqKnPQ63wltxsWtxuCpekfmZvvaPpY2CGBiIiIugOG4wzQlv7ACau+ppIHg7bqq/fvtRUVwVZQAKvPp4ZdbVObHoJZ5kBERETZjuE4QyTrD3zpMatx0YBVCB0xrfpGo8bXxKz65uUZq75WU2cHvX9vT+jdS0RERNTZGI7TQFEUdWqbacVXDgZxgXM7XhPGICJbYBEimFz4JuSAtupbWAhrfj5sPl9C8LVoq75ERERE1D4Mx53AXPJglD0Eg40dHhQF0FZ9RZsNFrcb1v798fq28YgoFlgkGZGoBR/2vhvX/wAt1voSERERUcdg4moDRZbV8BsMqh0etEluiETU1mYABKu1MfxqHR6s+fmNI4rNq75OJ555FnjxYwU3zhQwY7oF8+YrmPOUF5YcQdvM1rXmPi1DkpLf97z5CqJRpdkRxdRx+FwQERF1HYbjJGJ6++qjjOO7POgb3Ww22IuLYSsogC0/P7HkweuFaLM1e39qENaDsRqA9H/nPKXEfNxVJElIet/mY6WuweeCiIio62RlODa3OJNDISj6yq95hLGpy4O9d291o5vPZ6z2Stq/Fo+n3SUP0WhsMNbpH0ejCrq6DVqycJ4sxFPn43NBRETUdbIuHEfr69Gwa5cRfCWHA7Y+fWAtLIQ1Nzem3EFvdSZIUqceU3OnxNPZH9gcyp55VkE4DIaxNOFzQURE1DWyKhx7Ro6ErbAQ9uJidcKbx8MWZy2YMV0wwpjV2vXlHdSIzwUREVHny6pU6B05EgVnnQXPiBFwFBerJREMxs2aN78xjIXD6seUHnwuiIiIOh+TITXJXNf6vxUibpypbgxjKOt6fC6IiIi6RlaVVVDrZWIHjWzF54KIiKjrMBxTUpnYQSNb8bkgIiLqOoKiKF12XraysrKr7iphcILP5zPun4MTejbzc009F5/n7MHnOjvwec4e6XyufT5fi9dpUzr84osvcNNNN+Hkk0/GmDFjcPnll+ONN95oy011Gn1wQnxNpn6KWpK40kZEREREsVIuq1izZg1mzZoFq9WKyZMnw+v1Yvny5bj77ruxb98+/PCHP+yM40xZfE3mT+5MXrtJRERERKRLqawiEongwgsvxMGDB/HSSy9h5MiRAIC6ujpcffXV2LFjB5YuXYpBgwYl/fp0LKHrgVhvf8Vg3PPx1Fx24POcPfhcZwc+z9mjR5VVrF69Grt378aUKVOMYAwAHo8Ht912GyKRCBYuXJj6kXaiGdMFIxhzcAIRERERNSelcPzpp58CAE477bSEy0499dSY62QKDk4gIiIiotZKKRzv3LkTADBw4MCEy3Jzc+Hz+bBr164OObCOYK4x3ri2gIMTiIiIiKhZKW3Iq6urAwB4vd6kl3s8Hhw8eLDJr8/NzYXYReOaH3+iHnOeasCPbnPi1ltcAICf3JkPh6MejzzWAIfDYXyeep7W1BRR98fnOXvwuc4OfJ6zRyY/1106BKS6urrL7svvl3HjTAFXXxlEZWXQKP6++kogEBDg9zegsjLYZcdDXYebOrIDn+fswec6O/B5zh6ZviEvpXDs8XgAALW1tUkvr6ura3JVuas1N+BD3ZTHjXlEREREFCulGge9RVuyuuLq6mpUVlYmrUcmIiIiIuoOUgrHJ598MgDgo48+Srhs1apVAIDvfe97HXBYRERERERdL6VwPGHCBJSUlGDJkiX46quvjM/X1dXhscceg8ViwbRp0zr8IImIiIiIukJKNccWiwV//etfceONN+Kaa67BlClT4PF4sHz5cuzduxd33XUXjjrqqM46ViIiIiKiTpVyt4rx48fj+eefx0MPPYQ333wT4XAYQ4YMwZ133ompU6d2xjESEREREXWJNrVyO+644zBnzpyOPhYiIiIiorTqmokcRERERETdAMMxEREREZGG4ZiIiIj+f3v3GtPU+ccB/MsUMA04xXlJUKdJdzqQeEHnPUEE4xLvipjoEEWjeIuSzEQTjZc43RsnA/dCoujWzBvKYpZ5iy+8cbGKooI6Y4bQVicLGARJ2orP/4XndPRPwQJPabt8Pwlvnoc8/Z38PPI97dNziEjFcExEREREpGI4JiIiIiJSMRwTEREREakYjomIiIiIVAzHREREREQqhmMiIiIiIlWQEEL4uggiIiIiIn/Ad46JiIiIiFQMx0REREREKoZjIiIiIiIVwzERERERkYrhmIiIiIhIxXBMRERERKTq7usCOurBgwfIzs5GaWkpHA4H9Ho9UlNTMWvWLI/XeP/+PY4fP45Tp06hsrISOp0O48aNQ0ZGBoYMGeK94sljne3znTt3cOXKFZhMJlitVjQ2NiIyMhIJCQlYvXo1evbs6eUjIE/JOKebczgcSEpKwpMnTzB06FBcvHhRcsXUUbJ63dDQgNzcXFy+fBlmsxnBwcEYNGgQEhISsH79ei9VT56S0ec3b97g6NGjuHLlCiwWC0JCQjBw4EDMmzcPCxcuRGhoqBePgDxx7tw5lJSUoKysDE+fPoXD4cC+ffswf/78dq3jT5ksIO9zfOvWLaxYsQLBwcGYMWMGwsPDcfnyZVgsFmRkZCA9Pd2jdbZv347Tp09Dr9cjLi4ONTU1OH/+PEJDQ3Hy5Eno9XovHwm1RUafJ02ahNevX2P06NGIiopCUFAQTCYTHj16hMGDB+PkyZPo06dPFxwNtUXWOd3cjz/+iGPHjqGxsZHh2I/I6vWLFy+QmpoKs9mMiRMnIioqCna7HVVVVXjx4gV+//13Lx8JtUVGn9+8eYP58+fDbDZj9OjRGDFiBOx2O65fv46qqiqMHz8eR48exSef8ENwX5o6dSqsVit69+4NnU4Hq9XaoXDsV5lMBBiHwyESExNFTEyMKC8vd47X19eLGTNmiOjoaFFRUfHRdYqKioSiKGLx4sXCZrM5xwsLC4XBYBBLlizxRvnkIVl9PnTokHj16pXL2Pv378WOHTuEoihi586dskundpLV6+bKyspEdHS0+OWXX4SiKGL69OmSq6aOkNXrd+/eiQULFojhw4eLoqIit69DviOrzzk5OUJRFLF3716XcZvNJhYsWCAURREmk0l2+dROBQUFwmKxCCE+/M1VFEWcPXu2XWv4WyYLuMut4uJiVFVVYebMmYiOjnaOh4WFYe3atXj37h3y8/M/uk5eXh4AYNOmTQgJCXGOT5gwAZMnT8bt27dRUVEh/wDII7L6vGrVKvTr189lLCgoCGvXrgUA3L59W27h1G6yeq2x2+3YsmULRowYgW+++cYbJVMHyer1pUuX8PDhQ6SlpWH8+PEt5rt3D9gdg/8JsvpsNpsBAHFxcS7jISEhmDRpEgCgpqZGYuXUERMnTkRkZGSn1vC3TBZw4dhkMgEAJk+e3GJOO1m032nLrVu3oNPpEBsb22JOW5vByXdk9bk12h/Pbt26dXgNkkN2rw8ePIjKykp89913CAoKklMkSSGr1+fPnwcAfP3113j58iVOnDiBnJwcXLhwAW/fvpVYMXWErD5/8cUXAIAbN264jDscDhQWFqJHjx4YNWpUZ8slP+BvmSzgLq+fP38OAPj8889bzH366afo3bs3Kisr21yjsbER//zzDxRFcRuOtI3f2mtR15PR57acPXsWwL//UZPvyOz1gwcPcPjwYWRkZGDo0KEyyyQJZPW6rKwMAFBSUoJ9+/bBbrc75yIiIpCZmYlx48bJKZraTVafFy5ciHPnziE3NxdlZWWIiYmBw+HAjRs3UFdXh/3796N///6yy6cu5o+ZLODeOW5oaAAAhIeHu50PCwtDfX19m2to82FhYa2u0fy1qOvJ6HNrHj9+jJ9++gl9+vTBypUrO1wjySGr13a7HVu3bkVUVBTS0tKk1khyyOq19lH6nj17kJqaimvXrqGoqAjbtm1DfX091q1bh+rqanmFU7vI6nOPHj1gNBoxe/ZsmEwm5Obmwmg0OrdsuHuXkQKPP2aygAvHRJ1hNpuxevVqNDU14YcffkBERISvSyJJMjMzUVlZib1793K7zH+cUG+yNGXKFHz77bcYMGAAIiIikJKSgmXLlqG+vh5nzpzxcZXUWbW1tVi+fDnu37+PnJwc3LlzBwUFBdi1axfy8/ORnJyMuro6X5dJ/0EBF461K4jWrjobGhpavVrVaPOtXYVo461dxZD3yejz/7NarUhNTUVtbS2ysrLcfpGHup6MXpeXl+PYsWNIT0+HwWCQXiPJIeu81taZOnVqi7n4+HgA/269oK4nq8/ff/897t27h6ysLMTFxSE8PByfffYZkpOTsXnzZpjNZvz8889Sa6eu54+ZLODCsbb3xN1+pbq6Orx+/drtPqfmdDod+vbtC4vFgqamphbz2r4WPgjEd2T0uTmLxYKUlBRUV1cjMzPT+QeUfE9Gr//88080NTUhOzsbBoPB5QcAKioqYDAYMGbMGOn1k+dkndfafnJ3D/HRxmw2Wycqpc6Q1edr166hV69e+PLLL1vMaW9ulJeXd65Y8jl/zGQBF46/+uorAMDNmzdbzBUUFAAAxo4d+9F1xo4di8bGRty9e7fFnLa29lrU9WT1GfgQjJcuXYrq6mocOHAAiYmJ8gqlTpPR6yFDhiApKcntD/DhnYmkpCTMnTtXbvHULrLOay0YPXv2rMWcNtbZW0tRx8nqs91uR0NDg8sXLjW1tbUA4HLbLwpcfpfJuvSuyhI4HA6RkJAgYmJixKNHj5zjzW8u/tdffznHa2pqxLNnz0RNTY3LOv52w2lyJavPZrNZxMfHi+joaHHp0qUuq588J6vXreFDQPyHrF5XVVWJmJgYMWHCBPH333+7rDNnzhyhKIooLCz0/gGRW7L6nJaWJhRFEQcOHHAZt9lszjmj0ejVY6H2+dhDQAIlkwXk46OLi4uxcuVKBAcHY+bMmQgLC3M+lnLTpk1Ys2aN83ezs7Nx8OBBrF+/Hhs2bHBZZ9u2bcjLy/OPRxVSCzL6rD3WcuTIkW7vuQmgxb8L6nqyzml3DAYDHx/tR2T12mg0Ys+ePejVqxemTZuGkJAQXL16FVarFYsWLcLu3bu7+tCoGRl9fvz4MZYsWYK3b99i+PDhiI2Nhc1mw82bN2E2mzFs2DCcOHECoaGhvjhEUuXl5aGkpAQA8PTpU5SXlyM2Nta5dSYxMdH5iW2gZLKAu88x8OEjtePHjyMrKwsXLlyAw+GAXq/Hxo0bMXv2bI/X2b17NwwGA06dOgWj0QidTof4+HjeI9VPyOiz1WoFAJSWlqK0tNTt7zAc+56sc5r8n6xep6SkIDIyEkeOHMEff/yBpqYm6PV6pKenIzk52YtHQJ6Q0eeoqCjk5+fj0KFDKC4uxq+//opu3bph8ODB2LBhA1asWMFg7AdKSkrw22+/uYzdvXvXuUUiMjLSo+2M/pTJAvKdYyIiIiIibwi4L+QREREREXkLwzERERERkYrhmIiIiIhIxXBMRERERKRiOCYiIiIiUjEcExERERGpGI6JiIiIiFQMx0REREREKoZjIiIiIiIVwzERERERkYrhmIiIiIhIxXBMRERERKT6H7gjGS3ZCyFaAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(7, 5))\n",
    "\n",
    "# Plot data\n",
    "ax.plot(x_out, y_out, \"x\", label=\"data\")\n",
    "\n",
    "# Plot recovered linear regression\n",
    "x_range = np.linspace(min(x_out), max(x_out), 1000)\n",
    "y_pred = (\n",
    "    gauss_fitted.posterior.x.mean().item() * x_range\n",
    "    + gauss_fitted.posterior.Intercept.mean().item()\n",
    ")\n",
    "ax.plot(\n",
    "    x_range, y_pred, color=\"black\", linestyle=\"--\", label=\"Recovered regression line\"\n",
    ")\n",
    "\n",
    "# Plot HDIs\n",
    "for interval in [0.38, 0.68]:\n",
    "    az.plot_hdi(\n",
    "        x_out, gauss_fitted.posterior_predictive.y, hdi_prob=interval, color=\"firebrick\"\n",
    "    )\n",
    "\n",
    "# Plot true regression line\n",
    "ax.plot(x, true_regression_line, label=\"True regression line\", lw=2.0, color=\"black\")\n",
    "ax.legend(loc=0);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a8dc33cf",
   "metadata": {},
   "source": [
    "The recovered regression line, as well as the $0.5\\sigma$ and $1\\sigma$ bands are shown. \n",
    "\n",
    "Clearly there is skew in the fit. At lower $x$ values, the regression line is far higher than the true line. This is a result of the outliers, which cause the model to assume a higher value in that regime.\n",
    "\n",
    "Additionally the uncertainty bands are too wide (remember, the $1\\sigma$ band ought to cover 68% of the data, while here it covers most of the points). Due to the small probability mass in the tails of a normal distribution, the outliers have an large effect, causing the uncertainty bands to be oversized. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1ca15f83",
   "metadata": {},
   "source": [
    "Clearly, assuming the data are distributed normally is inducing problems here. Bayesian robust linear regression forgoes the normality assumption by instead using a Student T distribution to describe the distribution of the data. The Student T distribution has thicker tails, and by allocating more probability mass to the tails, outliers have a less strong effect.\n",
    "\n",
    "Comparing the two distributions,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "4e021729",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 720x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "normal_data = np.random.normal(loc=0, scale=1, size=100_000)\n",
    "t_data = np.random.standard_t(df=1, size=100_000)\n",
    "\n",
    "bins = np.arange(-8, 8, 0.15)\n",
    "plt.hist(normal_data, bins=bins, density=True, alpha=0.6, label=\"Normal\")\n",
    "plt.hist(t_data, bins=bins, density=True, alpha=0.6, label=\"Student T\")\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"Probability density\")\n",
    "plt.xlim(-8, 8)\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "643a5afb",
   "metadata": {},
   "source": [
    "As we can see, the tails of the Student T are much larger, which means values far from the mean are more likely when compared to the normal distribution.\n",
    "\n",
    "The T distribution is specified by a number of degrees of freedom ($\\nu$). In [`numpy.random.standard_t`](https://numpy.org/doc/stable/reference/random/generated/numpy.random.standard_t.html) this is the parameter `df`, in the [pymc T distribution](https://www.pymc.io/projects/docs/en/stable/api/distributions/generated/pymc.StudentT.html), it's `nu`. It is constrained to real numbers greater than 0. As the degrees of freedom increase, the probability in the tails Student T distribution decrease. In the limit of $\\nu \\rightarrow + \\infty$, the Student T distribution is a normal distribution. Below, the T distribution is plotted for various $\\nu$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "c51f3e1a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 720x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bins = np.arange(-8, 8, 0.15)\n",
    "for ndof in [0.1, 1, 10]:\n",
    "    t_data = np.random.standard_t(df=ndof, size=100_000)\n",
    "    plt.hist(t_data, bins=bins, density=True, label=f\"$\\\\nu = {ndof}$\", histtype=\"step\")\n",
    "\n",
    "plt.hist(normal_data, bins=bins, density=True, histtype=\"step\", label=\"Normal\")\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"Probability density\")\n",
    "plt.xlim(-6, 6)\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2f8bfa8b",
   "metadata": {},
   "source": [
    "In Bambi, the way to specify a regression with Student T distributed data is by passing `\"t\"` to the `family` parameter of a Model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "64ded684",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [nu, sigma, Intercept, x]\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "4c689e29740240638de584608dc4d763",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 1 seconds.\n"
     ]
    }
   ],
   "source": [
    "t_model = bmb.Model(\"y ~ x\", data, family=\"t\")\n",
    "t_fitted = t_model.fit(idata_kwargs={\"log_likelihood\": True})\n",
    "t_model.predict(t_fitted, kind=\"response\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "a1ed117e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>hdi_3%</th>\n",
       "      <th>hdi_97%</th>\n",
       "      <th>mcse_mean</th>\n",
       "      <th>mcse_sd</th>\n",
       "      <th>ess_bulk</th>\n",
       "      <th>ess_tail</th>\n",
       "      <th>r_hat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>nu</th>\n",
       "      <td>2.690</td>\n",
       "      <td>0.678</td>\n",
       "      <td>1.496</td>\n",
       "      <td>3.894</td>\n",
       "      <td>0.012</td>\n",
       "      <td>0.012</td>\n",
       "      <td>3188.0</td>\n",
       "      <td>2797.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sigma</th>\n",
       "      <td>0.468</td>\n",
       "      <td>0.055</td>\n",
       "      <td>0.374</td>\n",
       "      <td>0.580</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.001</td>\n",
       "      <td>3260.0</td>\n",
       "      <td>3116.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Intercept</th>\n",
       "      <td>1.018</td>\n",
       "      <td>0.119</td>\n",
       "      <td>0.794</td>\n",
       "      <td>1.242</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>4053.0</td>\n",
       "      <td>3165.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>x</th>\n",
       "      <td>1.785</td>\n",
       "      <td>0.200</td>\n",
       "      <td>1.403</td>\n",
       "      <td>2.155</td>\n",
       "      <td>0.003</td>\n",
       "      <td>0.003</td>\n",
       "      <td>4234.0</td>\n",
       "      <td>3388.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            mean     sd  hdi_3%  hdi_97%  mcse_mean  mcse_sd  ess_bulk  \\\n",
       "nu         2.690  0.678   1.496    3.894      0.012    0.012    3188.0   \n",
       "sigma      0.468  0.055   0.374    0.580      0.001    0.001    3260.0   \n",
       "Intercept  1.018  0.119   0.794    1.242      0.002    0.002    4053.0   \n",
       "x          1.785  0.200   1.403    2.155      0.003    0.003    4234.0   \n",
       "\n",
       "           ess_tail  r_hat  \n",
       "nu           2797.0    1.0  \n",
       "sigma        3116.0    1.0  \n",
       "Intercept    3165.0    1.0  \n",
       "x            3388.0    1.0  "
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.summary(t_fitted, var_names=\"~mu\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e655e175",
   "metadata": {},
   "source": [
    "Note the new parameter in the model, `y_nu`. This is the aforementioned degrees of freedom. If this number were very high, we would expect it to be well described by a normal distribution. However, the HDI of this spans from 1.5 to 3.7, meaning that the tails are much heavier than a normal distribution. As a result of the heavier tails, `y_sigma` has also dropped precipitously from the normal model, meaning the oversized uncertainty bands from above have shrunk.\n",
    "\n",
    "\n",
    "Comparing the extracted values of the two models,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "4e88de57",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>Model</th>\n",
       "      <th>True</th>\n",
       "      <th>Normal</th>\n",
       "      <th>T</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Slope</th>\n",
       "      <td>2.0</td>\n",
       "      <td>1.15</td>\n",
       "      <td>1.79</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Intercept</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.51</td>\n",
       "      <td>1.02</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Model      True  Normal     T\n",
       "Slope       2.0    1.15  1.79\n",
       "Intercept   1.0    1.51  1.02"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def get_slope_intercept(mod):\n",
    "    return (mod.posterior.x.mean().item(), mod.posterior.Intercept.mean().item())\n",
    "\n",
    "gauss_slope, gauss_int = get_slope_intercept(gauss_fitted)\n",
    "t_slope, t_int = get_slope_intercept(t_fitted)\n",
    "\n",
    "pd.DataFrame(\n",
    "    {\n",
    "        \"Model\": [\"True\", \"Normal\", \"T\"],\n",
    "        \"Slope\": [2, gauss_slope, t_slope],\n",
    "        \"Intercept\": [1, gauss_int, t_int],\n",
    "    }\n",
    ").set_index(\"Model\").T.round(decimals=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "21396175",
   "metadata": {},
   "source": [
    "Here we can see the mean recovered values of both the slope and intercept are far closer to the true values using the robust regression model compared to the normally distributed one.\n",
    "\n",
    "Visually comparing the robust regression line,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "ce58148c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(7, 5))\n",
    "\n",
    "# Plot data\n",
    "ax.plot(x_out, y_out, \"x\", label=\"data\")\n",
    "\n",
    "# Plot recovered linear regression\n",
    "x_range = np.linspace(min(x_out), max(x_out), 1000)\n",
    "y_pred = (\n",
    "    t_fitted.posterior.x.mean().item() * x_range\n",
    "    + t_fitted.posterior.Intercept.mean().item()\n",
    ")\n",
    "ax.plot(\n",
    "    x_range, y_pred, color=\"black\", linestyle=\"--\", label=\"Recovered regression line\"\n",
    ")\n",
    "\n",
    "# Plot HDIs\n",
    "for interval in [0.38, 0.68]:\n",
    "    az.plot_hdi(\n",
    "        x_out, t_fitted.posterior_predictive.y, hdi_prob=interval, color=\"firebrick\"\n",
    "    )\n",
    "\n",
    "# Plot true regression line\n",
    "ax.plot(x, true_regression_line, label=\"True regression line\", lw=2.0, color=\"black\")\n",
    "ax.legend(loc=0);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e7b65b16",
   "metadata": {},
   "source": [
    "This is much better. The true and recovered regression lines are much closer, and the uncertainty bands are appropriate sized. The effect of the outliers is not _entirely_ gone, the recovered line still slightly differs from the true line, but the effect is far smaller, which is a result of the Student T likelihood function ascribing a higher probability to outliers than the normal distribution. Additionally, this inference is based on sampling methods, so it is expected to have small differences (especially given a relatively small number of samples).\n",
    "\n",
    "Last, another way to evaluate the models is to compare based on Leave-one-out Cross-validation (LOO), which provides an estimate of accuracy on out-of-sample predictions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "855b0070",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/arviz/stats/stats.py:797: UserWarning: Estimated shape parameter of Pareto distribution is greater than 0.70 for one or more samples. You should consider using a more robust model, this is because importance sampling is less likely to work well if the marginal posterior and LOO posterior are very different. This is more likely to happen with a non-robust model and highly influential observations.\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>rank</th>\n",
       "      <th>elpd_loo</th>\n",
       "      <th>p_loo</th>\n",
       "      <th>elpd_diff</th>\n",
       "      <th>weight</th>\n",
       "      <th>se</th>\n",
       "      <th>dse</th>\n",
       "      <th>warning</th>\n",
       "      <th>scale</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Student T</th>\n",
       "      <td>0</td>\n",
       "      <td>-115.132811</td>\n",
       "      <td>5.146747</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.0</td>\n",
       "      <td>14.413946</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>False</td>\n",
       "      <td>log</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gaussian</th>\n",
       "      <td>1</td>\n",
       "      <td>-174.486283</td>\n",
       "      <td>13.466794</td>\n",
       "      <td>59.353472</td>\n",
       "      <td>0.0</td>\n",
       "      <td>28.033136</td>\n",
       "      <td>16.78544</td>\n",
       "      <td>True</td>\n",
       "      <td>log</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           rank    elpd_loo      p_loo  elpd_diff  weight         se  \\\n",
       "Student T     0 -115.132811   5.146747   0.000000     1.0  14.413946   \n",
       "gaussian      1 -174.486283  13.466794  59.353472     0.0  28.033136   \n",
       "\n",
       "                dse  warning scale  \n",
       "Student T   0.00000    False   log  \n",
       "gaussian   16.78544     True   log  "
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "models = {\n",
    "    \"gaussian\": gauss_fitted,\n",
    "    \"Student T\": t_fitted\n",
    "}\n",
    "df_compare = az.compare(models)\n",
    "df_compare"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "f1f1e08f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 600x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "az.plot_compare(df_compare, insample_dev=False);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2b62d1df",
   "metadata": {},
   "source": [
    "Here it is quite obvious that the Student T model is much better, due to having a clearly larger value of LOO."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "05e70949",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Last updated: Sun Sep 28 2025\n",
      "\n",
      "Python implementation: CPython\n",
      "Python version       : 3.13.7\n",
      "IPython version      : 9.4.0\n",
      "\n",
      "bambi     : 0.14.1.dev58+gb25742785.d20250928\n",
      "arviz     : 0.22.0\n",
      "pandas    : 2.3.2\n",
      "matplotlib: 3.10.6\n",
      "numpy     : 2.3.3\n",
      "\n",
      "Watermark: 2.5.0\n",
      "\n"
     ]
    }
   ],
   "source": [
    "%load_ext watermark\n",
    "%watermark -n -u -v -iv -w"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "dev",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.13.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
